Number Theory Tables, Department of Mathematics and Statistics, UNCG

Number of totally ramified extensions of Q(δ)≅Q2[x]/(x2+x+1) of degree 8

Introduction
Extensions of Q2 of degree 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 32
Extensions of Q2[x]/(x2+x+1) of degree 2, 4, 8 Extensions of Q2[x]/(x4+x+1) of degree 2, 4, 8
Extensions of Q3 of degree 3, 6, 9, 12, 15, 18, 21, 24, 27     Extensions of Q3[x]/(x2+2x+2) of degree 3, 6, 9
Extensions of Q5 of degree 5, 10, 15, 20, 25, 30, 35, 50, Extensions of Q7 of degree 7, 14, 21, 49
Extensions of Q11 of degree 11, 22, 33, Extensions of Q13 of degree 13, 26, 39,
Extensions of Q17 of degree 17, 34 Extensions of Q19 of degree 19,

Polynomial Invariants #Aut Splitting Field Number of
j Ramification Polygon Slopes Residual Polynomials fT eT #Gal Gal Polynomials Extensions
1{(1,1), (8,0)}[ 1/7 ](z+1){1}37{ 168 }{ 8T36 }1233·233·23
(z+δ){1}37{ 168 }{ 8T36 }123
(z+(δ+1)){1}37{ 168 }{ 8T36 }123
3{(1,3), (2,2), (8,0)}[ 1, 1/3 ](z+1, z2+1){2}132239·233·25
(δz+1, z2+δ){2}13223
((δ+1)z+1, z2+(δ+1)){2}13223
(z+δ, z2+1){2}13223
(δz+δ, z2+δ){2}13223
((δ+1)z+δ, z2+(δ+1)){2}13223
(z+(δ+1), z2+1){2}13223
(δz+(δ+1), z2+δ){2}13223
((δ+1)z+(δ+1), z2+(δ+1)){2}13223
{(1,3), (8,0)}[ 3/7 ](z+1){1}37{ 168 }{ 8T36 }1233·23
(z+δ){1}37{ 168 }{ 8T36 }123
(z+(δ+1)){1}37{ 168 }{ 8T36 }123
5{(1,5), (2,2), (8,0)}[ 3, 1/3 ](z+1, z2+1){2}1323259·253·27
(δz+1, z2+δ){2}132325
((δ+1)z+1, z2+(δ+1)){2}132325
(z+δ, z2+1){2}132325
(δz+δ, z2+δ){2}132325
((δ+1)z+δ, z2+(δ+1)){2}132325
(z+(δ+1), z2+1){2}132325
(δz+(δ+1), z2+δ){2}132325
((δ+1)z+(δ+1), z2+(δ+1)){2}132325
{(1,5), (8,0)}[ 5/7 ](z+1){1}37{ 168 }{ 8T36 }22253·25
(z+δ){1}37{ 168 }{ 8T36 }2225
(z+(δ+1)){1}37{ 168 }{ 8T36 }2225
7{(1,7), (2,2), (8,0)}[ 5, 1/3 ](z+1, z2+1){2}1325279·273·29
(δz+1, z2+δ){2}132527
((δ+1)z+1, z2+(δ+1)){2}132527
(z+δ, z2+1){2}132527
(δz+δ, z2+δ){2}132527
((δ+1)z+δ, z2+(δ+1)){2}132527
(z+(δ+1), z2+1){2}132527
(δz+(δ+1), z2+δ){2}132527
((δ+1)z+(δ+1), z2+(δ+1)){2}132527
{(1,7), (2,6), (4,4), (8,0)}[ 1 ](z7+z3+z+1){4}21{ 16 }{ 8T9 }222327·23
(z7+δz3+z+1){1}71{ 56 }{ 8T25 }123
(z7+(δ+1)z3+z+1){1}71{ 56 }{ 8T25 }123
(z7+z3+δz+1){1}71{ 56 }{ 8T25 }123
(z7+δz3+δz+1){2}31{ 24 }{ 8T13 }223
(z7+(δ+1)z3+δz+1){2}31{ 24 }{ 8T13 }223
(z7+z3+(δ+1)z+1){1}71{ 56 }{ 8T25 }123
(z7+δz3+(δ+1)z+1){2}31{ 24 }{ 8T13 }223
(z7+(δ+1)z3+(δ+1)z+1){2}31{ 24 }{ 8T13 }223
(z7+z3+z+δ){1}71{ 56 }{ 8T25 }123
(z7+δz3+z+δ){4}21{ 16 }{ 8T9 }2223
(z7+(δ+1)z3+z+δ){1}71{ 56 }{ 8T25 }123
(z7+z3+δz+δ){2}31{ 24 }{ 8T13 }223
(z7+δz3+δz+δ){1}71{ 56 }{ 8T25 }123
(z7+(δ+1)z3+δz+δ){2}31{ 24 }{ 8T13 }223
(z7+z3+(δ+1)z+δ){2}31{ 24 }{ 8T13 }223
(z7+δz3+(δ+1)z+δ){1}71{ 56 }{ 8T25 }123
(z7+(δ+1)z3+(δ+1)z+δ){2}31{ 24 }{ 8T13 }223
(z7+z3+z+(δ+1)){1}71{ 56 }{ 8T25 }123
(z7+δz3+z+(δ+1)){1}71{ 56 }{ 8T25 }123
(z7+(δ+1)z3+z+(δ+1)){4}21{ 16 }{ 8T9 }2223
(z7+z3+δz+(δ+1)){2}31{ 24 }{ 8T13 }223
(z7+δz3+δz+(δ+1)){2}31{ 24 }{ 8T13 }223
(z7+(δ+1)z3+δz+(δ+1)){1}71{ 56 }{ 8T25 }123
(z7+z3+(δ+1)z+(δ+1)){2}31{ 24 }{ 8T13 }223
(z7+δz3+(δ+1)z+(δ+1)){2}31{ 24 }{ 8T13 }223
(z7+(δ+1)z3+(δ+1)z+(δ+1)){1}71{ 56 }{ 8T25 }123
{(1,7), (4,4), (8,0)}[ 1 ](z7+z3+1){1}71{ 56 }{ 8T25 }1239·23
(z7+δz3+1){2}41{ 32 }{ 8T19 }223
(z7+(δ+1)z3+1){2}41{ 32 }{ 8T19 }223
(z7+z3+δ){2}41{ 32 }{ 8T19 }223
(z7+δz3+δ){1}71{ 56 }{ 8T25 }123
(z7+(δ+1)z3+δ){2}41{ 32 }{ 8T19 }223
(z7+z3+(δ+1)){2}41{ 32 }{ 8T19 }223
(z7+δz3+(δ+1)){2}41{ 32 }{ 8T19 }223
(z7+(δ+1)z3+(δ+1)){1}71{ 56 }{ 8T25 }123
{(1,7), (2,6), (8,0)}[ 1 ](z7+z+1){1}71{ 56 }{ 8T25 }1239·23
(z7+δz+1){2}41{ 32 }{ 8T19 }223
(z7+(δ+1)z+1){2}41{ 32 }{ 8T19 }223
(z7+z+δ){1}71{ 56 }{ 8T25 }123
(z7+δz+δ){2}41{ 32 }{ 8T19 }223
(z7+(δ+1)z+δ){2}41{ 32 }{ 8T19 }223
(z7+z+(δ+1)){1}71{ 56 }{ 8T25 }123
(z7+δz+(δ+1)){2}41{ 32 }{ 8T19 }223
(z7+(δ+1)z+(δ+1)){2}41{ 32 }{ 8T19 }223
{(1,7), (8,0)}[ 1 ](z7+1){2}31{ 24 }{ 8T13 }2233·23
(z7+δ){2}31{ 24 }{ 8T13 }223
(z7+(δ+1)){2}31{ 24 }{ 8T13 }223
9{(1,9), (2,2), (8,0)}[ 7, 1/3 ](z+1, z2+1){2}1327 [.]299·293·211
(δz+1, z2+δ){2}1327 [.]29
((δ+1)z+1, z2+(δ+1)){2}1327 [.]29
(z+δ, z2+1){2}1327 [.]29
(δz+δ, z2+δ){2}1327 [.]29
((δ+1)z+δ, z2+(δ+1)){2}1327 [.]29
(z+(δ+1), z2+1){2}1327 [.]29
(δz+(δ+1), z2+δ){2}1327 [.]29
((δ+1)z+(δ+1), z2+(δ+1)){2}1327 [.]29
{(1,9), (2,6), (4,4), (8,0)}[ 3, 1 ](z+1, z6+z2+1){2}31232527·25
(z+1, z6+δz2+1){2}312325
(z+1, z6+(δ+1)z2+1){2}312325
(δz+1, z6+z2+δ){2}2124 [23]25
(δz+1, z6+δz2+δ){2}2124 [23]25
(δz+1, z6+(δ+1)z2+δ){2}2124 [23]25
((δ+1)z+1, z6+z2+(δ+1)){2}2124 [23]25
((δ+1)z+1, z6+δz2+(δ+1)){2}2124 [23]25
((δ+1)z+1, z6+(δ+1)z2+(δ+1)){2}2124 [23]25
(z+δ, z6+z2+1){2}312325
(z+δ, z6+δz2+1){2}312325
(z+δ, z6+(δ+1)z2+1){2}312325
(δz+δ, z6+z2+δ){2,4}2124 [3·22]25
(δz+δ, z6+δz2+δ){2,4}2124 [3·22]25
(δz+δ, z6+(δ+1)z2+δ){2,4}2124 [3·22]25
((δ+1)z+δ, z6+z2+(δ+1)){2}2124 [23]25
((δ+1)z+δ, z6+δz2+(δ+1)){2}2124 [23]25
((δ+1)z+δ, z6+(δ+1)z2+(δ+1)){2}2124 [23]25
(z+(δ+1), z6+z2+1){2}312325
(z+(δ+1), z6+δz2+1){2}312325
(z+(δ+1), z6+(δ+1)z2+1){2}312325
(δz+(δ+1), z6+z2+δ){2}2124 [23]25
(δz+(δ+1), z6+δz2+δ){2}2124 [23]25
(δz+(δ+1), z6+(δ+1)z2+δ){2}2124 [23]25
((δ+1)z+(δ+1), z6+z2+(δ+1)){2,4}2124 [3·22]25
((δ+1)z+(δ+1), z6+δz2+(δ+1)){2,4}2124 [3·22]25
((δ+1)z+(δ+1), z6+(δ+1)z2+(δ+1)){2,4}2124 [3·22]25
{(1,9), (4,4), (8,0)}[ 5/3, 1 ](z+1, z4+1){1}1323 [22]259·25
(δz+1, z4+δ){1}1323 [22]25
((δ+1)z+1, z4+(δ+1)){1}1323 [22]25
(z+δ, z4+1){1}1323 [22]25
(δz+δ, z4+δ){1}1323 [22]25
((δ+1)z+δ, z4+(δ+1)){1}1323 [22]25
(z+(δ+1), z4+1){1}1323 [22]25
(δz+(δ+1), z4+δ){1}1323 [22]25
((δ+1)z+(δ+1), z4+(δ+1)){1}1323 [22]25
{(1,9), (2,6), (8,0)}[ 3, 1 ](z+1, z6+1){4,8}1125 [5·22]259·25
(δz+1, z6+δ){2}312325
((δ+1)z+1, z6+(δ+1)){2}312325
(z+δ, z6+1){2}1125 [23]25
(δz+δ, z6+δ){2}312325
((δ+1)z+δ, z6+(δ+1)){2}312325
(z+(δ+1), z6+1){2}1125 [23]25
(δz+(δ+1), z6+δ){2}312325
((δ+1)z+(δ+1), z6+(δ+1)){2}312325
10{(1,10), (2,2), (8,0)}[ 8, 1/3 ](z+1, z2+1){2}1329 [.]2113·2113·211
(δz+δ, z2+δ){2}1329 [.]211
((δ+1)z+(δ+1), z2+(δ+1)){2}1329 [.]211
11{(1,11), (2,6), (4,4), (8,0)}[ 5, 1 ](z+1, z6+z2+1){2}3125 [.]2727·273·211
(z+1, z6+δz2+1){2}3125 [.]27
(z+1, z6+(δ+1)z2+1){2}3125 [.]27
(δz+1, z6+z2+δ){2,4}2126 [5·23]27
(δz+1, z6+δz2+δ){2,4}2126 [5·23]27
(δz+1, z6+(δ+1)z2+δ){2,4}2126 [5·23]27
((δ+1)z+1, z6+z2+(δ+1)){2,4}2126 [5·23]27
((δ+1)z+1, z6+δz2+(δ+1)){2,4}2126 [5·23]27
((δ+1)z+1, z6+(δ+1)z2+(δ+1)){2,4}2126 [5·23]27
(z+δ, z6+z2+1){2}3125 [.]27
(z+δ, z6+δz2+1){2}3125 [.]27
(z+δ, z6+(δ+1)z2+1){2}3125 [.]27
(δz+δ, z6+z2+δ){2,4}2126 [5·23]27
(δz+δ, z6+δz2+δ){2,4}2126 [5·23]27
(δz+δ, z6+(δ+1)z2+δ){2,4}2126 [5·23]27
((δ+1)z+δ, z6+z2+(δ+1)){2,4}2126 [5·23]27
((δ+1)z+δ, z6+δz2+(δ+1)){2,4}2126 [5·23]27
((δ+1)z+δ, z6+(δ+1)z2+(δ+1)){2,4}2126 [5·23]27
(z+(δ+1), z6+z2+1){2}3125 [.]27
(z+(δ+1), z6+δz2+1){2}3125 [.]27
(z+(δ+1), z6+(δ+1)z2+1){2}3125 [.]27
(δz+(δ+1), z6+z2+δ){2,4}2126 [5·23]27
(δz+(δ+1), z6+δz2+δ){2,4}2126 [5·23]27
(δz+(δ+1), z6+(δ+1)z2+δ){2,4}2126 [5·23]27
((δ+1)z+(δ+1), z6+z2+(δ+1)){2,4}2126 [5·23]27
((δ+1)z+(δ+1), z6+δz2+(δ+1)){2,4}2126 [5·23]27
((δ+1)z+(δ+1), z6+(δ+1)z2+(δ+1)){2,4}2126 [5·23]27
{(1,11), (4,4), (8,0)}[ 7/3, 1 ](z+1, z4+1){1,2}1325 [5·22]279·27
(δz+1, z4+δ){1,2}1325 [5·22]27
((δ+1)z+1, z4+(δ+1)){1,2}1325 [5·22]27
(z+δ, z4+1){1,2}1325 [5·22]27
(δz+δ, z4+δ){1,2}1325 [5·22]27
((δ+1)z+δ, z4+(δ+1)){1,2}1325 [5·22]27
(z+(δ+1), z4+1){1,2}1325 [5·22]27
(δz+(δ+1), z4+δ){1,2}1325 [5·22]27
((δ+1)z+(δ+1), z4+(δ+1)){1,2}1325 [5·22]27
{(1,11), (2,6), (8,0)}[ 5, 1 ](z+1, z6+1){2,4,8}1127 [7·23]279·27
(δz+1, z6+δ){2}3125 [.]27
((δ+1)z+1, z6+(δ+1)){2}3125 [.]27
(z+δ, z6+1){2,4,8}1127 [7·23]27
(δz+δ, z6+δ){2}3125 [.]27
((δ+1)z+δ, z6+(δ+1)){2}3125 [.]27
(z+(δ+1), z6+1){2,4,8}1127 [7·23]27
(δz+(δ+1), z6+δ){2}3125 [.]27
((δ+1)z+(δ+1), z6+(δ+1)){2}3125 [.]27
13{(1,13), (2,6), (4,4), (8,0)}[ 7, 1 ](z+1, z6+z2+1){2}3127 [.]2927·293·213
(z+1, z6+δz2+1){2}3127 [.]29
(z+1, z6+(δ+1)z2+1){2}3127 [.]29
(δz+1, z6+z2+δ){2,4}2128 [5·25]29
(δz+1, z6+δz2+δ){2}2128 [27]29
(δz+1, z6+(δ+1)z2+δ){2}2128 [27]29
((δ+1)z+1, z6+z2+(δ+1)){2,4}2128 [5·25]29
((δ+1)z+1, z6+δz2+(δ+1)){2}2128 [27]29
((δ+1)z+1, z6+(δ+1)z2+(δ+1)){2}2128 [27]29
(z+δ, z6+z2+1){2}3127 [.]29
(z+δ, z6+δz2+1){2}3127 [.]29
(z+δ, z6+(δ+1)z2+1){2}3127 [.]29
(δz+δ, z6+z2+δ){2}2128 [27]29
(δz+δ, z6+δz2+δ){2}2128 [27]29
(δz+δ, z6+(δ+1)z2+δ){2,4}2128 [5·25]29
((δ+1)z+δ, z6+z2+(δ+1)){2}2128 [27]29
((δ+1)z+δ, z6+δz2+(δ+1)){2}2128 [27]29
((δ+1)z+δ, z6+(δ+1)z2+(δ+1)){2,4}2128 [5·25]29
(z+(δ+1), z6+z2+1){2}3127 [.]29
(z+(δ+1), z6+δz2+1){2}3127 [.]29
(z+(δ+1), z6+(δ+1)z2+1){2}3127 [.]29
(δz+(δ+1), z6+z2+δ){2}2128 [27]29
(δz+(δ+1), z6+δz2+δ){2,4}2128 [5·25]29
(δz+(δ+1), z6+(δ+1)z2+δ){2}2128 [27]29
((δ+1)z+(δ+1), z6+z2+(δ+1)){2}2128 [27]29
((δ+1)z+(δ+1), z6+δz2+(δ+1)){2,4}2128 [5·25]29
((δ+1)z+(δ+1), z6+(δ+1)z2+(δ+1)){2}2128 [27]29
{(1,13), (2,10), (4,4), (8,0)}[ 3, 1 ](z3+z+1, z4+1){1}3125 [24]2727·27
(δz3+z+1, z4+δ){2}2126 [25]27
((δ+1)z3+z+1, z4+(δ+1)){2}2126 [25]27
(z3+δz+1, z4+1){1}3125 [24]27
(δz3+δz+1, z4+δ){2}2126 [25]27
((δ+1)z3+δz+1, z4+(δ+1)){2}2126 [25]27
(z3+(δ+1)z+1, z4+1){1}3125 [24]27
(δz3+(δ+1)z+1, z4+δ){2}2126 [25]27
((δ+1)z3+(δ+1)z+1, z4+(δ+1)){2}2126 [25]27
(z3+z+δ, z4+1){2}2126 [25]27
(δz3+z+δ, z4+δ){1}3125 [24]27
((δ+1)z3+z+δ, z4+(δ+1)){2,4}2126 [3·24]27
(z3+δz+δ, z4+1){2}2126 [25]27
(δz3+δz+δ, z4+δ){1}3125 [24]27
((δ+1)z3+δz+δ, z4+(δ+1)){2}2126 [25]27
(z3+(δ+1)z+δ, z4+1){2}2126 [25]27
(δz3+(δ+1)z+δ, z4+δ){1}3125 [24]27
((δ+1)z3+(δ+1)z+δ, z4+(δ+1)){2}2126 [25]27
(z3+z+(δ+1), z4+1){2}2126 [25]27
(δz3+z+(δ+1), z4+δ){2,4}2126 [3·24]27
((δ+1)z3+z+(δ+1), z4+(δ+1)){1}3125 [24]27
(z3+δz+(δ+1), z4+1){2}2126 [25]27
(δz3+δz+(δ+1), z4+δ){2}2126 [25]27
((δ+1)z3+δz+(δ+1), z4+(δ+1)){1}3125 [24]27
(z3+(δ+1)z+(δ+1), z4+1){2}2126 [25]27
(δz3+(δ+1)z+(δ+1), z4+δ){2}2126 [25]27
((δ+1)z3+(δ+1)z+(δ+1), z4+(δ+1)){1}3125 [24]27
{(1,13), (2,6), (8,0)}[ 7, 1 ](z+1, z6+1){2,4}1129 [5·25]299·29
(δz+1, z6+δ){2}3127 [.]29
((δ+1)z+1, z6+(δ+1)){2}3127 [.]29
(z+δ, z6+1){2,4}1129 [5·25]29
(δz+δ, z6+δ){2}3127 [.]29
((δ+1)z+δ, z6+(δ+1)){2}3127 [.]29
(z+(δ+1), z6+1){2,4}1129 [5·25]29
(δz+(δ+1), z6+δ){2}3127 [.]29
((δ+1)z+(δ+1), z6+(δ+1)){2}3127 [.]29
14{(1,14), (2,6), (4,4), (8,0)}[ 8, 1 ](z+1, z6+z2+1){2}3129 [.]2119·2113·213
(z+1, z6+δz2+1){2}3129 [.]211
(z+1, z6+(δ+1)z2+1){2}3129 [.]211
(δz+δ, z6+z2+δ){2}21210 [29]211
(δz+δ, z6+δz2+δ){2}21210 [29]211
(δz+δ, z6+(δ+1)z2+δ){2}21210 [29]211
((δ+1)z+(δ+1), z6+z2+(δ+1)){2}21210 [29]211
((δ+1)z+(δ+1), z6+δz2+(δ+1)){2}21210 [29]211
((δ+1)z+(δ+1), z6+(δ+1)z2+(δ+1)){2}21210 [29]211
{(1,14), (2,6), (8,0)}[ 8, 1 ](z+1, z6+1){2,4,8}11211 [?]2113·211
(δz+δ, z6+δ){2}3129 [.]211
((δ+1)z+(δ+1), z6+(δ+1)){2}3129 [.]211
15{(1,15), (2,10), (4,4), (8,0)}[ 5, 3, 1 ](z+1, z2+1, z4+1){2,4,8}1129 [7·25]2927·293·213
(z+1, δz2+1, z4+δ){2}1129 [27]29
(z+1, (δ+1)z2+1, z4+(δ+1)){2}1129 [27]29
(δz+1, z2+δ, z4+1){2}1129 [27]29
(δz+1, δz2+δ, z4+δ){2}1129 [27]29
(δz+1, (δ+1)z2+δ, z4+(δ+1)){2,4,8}1129 [7·25]29
((δ+1)z+1, z2+(δ+1), z4+1){2}1129 [27]29
((δ+1)z+1, δz2+(δ+1), z4+δ){2,4,8}1129 [7·25]29
((δ+1)z+1, (δ+1)z2+(δ+1), z4+(δ+1)){2}1129 [27]29
(z+δ, z2+1, z4+1){2,4}1129 [5·25]29
(z+δ, δz2+1, z4+δ){2}1129 [27]29
(z+δ, (δ+1)z2+1, z4+(δ+1)){2,4}1129 [3·26]29
(δz+δ, z2+δ, z4+1){2}1129 [27]29
(δz+δ, δz2+δ, z4+δ){2,4}1129 [3·26]29
(δz+δ, (δ+1)z2+δ, z4+(δ+1)){2,4}1129 [5·25]29
((δ+1)z+δ, z2+(δ+1), z4+1){2,4}1129 [3·26]29
((δ+1)z+δ, δz2+(δ+1), z4+δ){2,4}1129 [5·25]29
((δ+1)z+δ, (δ+1)z2+(δ+1), z4+(δ+1)){2}1129 [27]29
(z+(δ+1), z2+1, z4+1){2,4}1129 [5·25]29
(z+(δ+1), δz2+1, z4+δ){2,4}1129 [3·26]29
(z+(δ+1), (δ+1)z2+1, z4+(δ+1)){2}1129 [27]29
(δz+(δ+1), z2+δ, z4+1){2,4}1129 [3·26]29
(δz+(δ+1), δz2+δ, z4+δ){2}1129 [27]29
(δz+(δ+1), (δ+1)z2+δ, z4+(δ+1)){2,4}1129 [5·25]29
((δ+1)z+(δ+1), z2+(δ+1), z4+1){2}1129 [27]29
((δ+1)z+(δ+1), δz2+(δ+1), z4+δ){2,4}1129 [5·25]29
((δ+1)z+(δ+1), (δ+1)z2+(δ+1), z4+(δ+1)){2,4}1129 [3·26]29
{(1,15), (2,12), (4,4), (8,0)}[ 3, 4, 1 ](z+1, z2+1, z4+1){1}1328 [26]299·29
(δz+1, δz2+δ, z4+δ){1}1328 [26]29
((δ+1)z+1, (δ+1)z2+(δ+1), z4+(δ+1)){1}1328 [26]29
(z+δ, z2+1, z4+1){1}1328 [26]29
(δz+δ, δz2+δ, z4+δ){1}1328 [26]29
((δ+1)z+δ, (δ+1)z2+(δ+1), z4+(δ+1)){1}1328 [26]29
(z+(δ+1), z2+1, z4+1){1}1328 [26]29
(δz+(δ+1), δz2+δ, z4+δ){1}1328 [26]29
((δ+1)z+(δ+1), (δ+1)z2+(δ+1), z4+(δ+1)){1}1328 [26]29
{(1,15), (2,10), (4,8), (8,0)}[ 5, 1, 2 ](z+1, z2+1, z4+1){2}1329 [27]299·29
(δz+1, z2+δ, z4+1){2}1329 [27]29
((δ+1)z+1, z2+(δ+1), z4+1){2}1329 [27]29
(z+δ, z2+1, z4+1){2}1329 [27]29
(δz+δ, z2+δ, z4+1){2}1329 [27]29
((δ+1)z+δ, z2+(δ+1), z4+1){2}1329 [27]29
(z+(δ+1), z2+1, z4+1){2}1329 [27]29
(δz+(δ+1), z2+δ, z4+1){2}1329 [27]29
((δ+1)z+(δ+1), z2+(δ+1), z4+1){2}1329 [27]29
{(1,15), (4,8), (8,0)}[ 7/3, 2 ](z+1, z4+1){1}1327 [26]293·29
(z+δ, z4+1){1}1327 [26]29
(z+(δ+1), z4+1){1}1327 [26]29
17{(1,17), (2,10), (4,4), (8,0)}[ 7, 3, 1 ](z+1, z2+1, z4+1){2,4,8}11211 [?]21127·2113·215
(z+1, δz2+1, z4+δ){2,4,8}11211 [?]211
(z+1, (δ+1)z2+1, z4+(δ+1)){2,4,8}11211 [?]211
(δz+1, z2+δ, z4+1){2,4,8}11211 [?]211
(δz+1, δz2+δ, z4+δ){2,4,8}11211 [?]211
(δz+1, (δ+1)z2+δ, z4+(δ+1)){2,4,8}11211 [?]211
((δ+1)z+1, z2+(δ+1), z4+1){2,4,8}11211 [?]211
((δ+1)z+1, δz2+(δ+1), z4+δ){2,4,8}11211 [?]211
((δ+1)z+1, (δ+1)z2+(δ+1), z4+(δ+1)){2,4,8}11211 [?]211
(z+δ, z2+1, z4+1){2,4,8}11211 [?]211
(z+δ, δz2+1, z4+δ){2,4,8}11211 [?]211
(z+δ, (δ+1)z2+1, z4+(δ+1)){2,4,8}11211 [?]211
(δz+δ, z2+δ, z4+1){2,4,8}11211 [?]211
(δz+δ, δz2+δ, z4+δ){2,4,8}11211 [?]211
(δz+δ, (δ+1)z2+δ, z4+(δ+1)){2,4,8}11211 [?]211
((δ+1)z+δ, z2+(δ+1), z4+1){2,4,8}11211 [?]211
((δ+1)z+δ, δz2+(δ+1), z4+δ){2,4,8}11211 [?]211
((δ+1)z+δ, (δ+1)z2+(δ+1), z4+(δ+1)){2,4,8}11211 [?]211
(z+(δ+1), z2+1, z4+1){2,4,8}11211 [?]211
(z+(δ+1), δz2+1, z4+δ){2,4,8}11211 [?]211
(z+(δ+1), (δ+1)z2+1, z4+(δ+1)){2,4,8}11211 [?]211
(δz+(δ+1), z2+δ, z4+1){2,4,8}11211 [?]211
(δz+(δ+1), δz2+δ, z4+δ){2,4,8}11211 [?]211
(δz+(δ+1), (δ+1)z2+δ, z4+(δ+1)){2,4,8}11211 [?]211
((δ+1)z+(δ+1), z2+(δ+1), z4+1){2,4,8}11211 [?]211
((δ+1)z+(δ+1), δz2+(δ+1), z4+δ){2,4,8}11211 [?]211
((δ+1)z+(δ+1), (δ+1)z2+(δ+1), z4+(δ+1)){2,4,8}11211 [?]211
{(1,17), (2,12), (4,4), (8,0)}[ 5, 4, 1 ](z+1, z2+1, z4+1){2,4,8}11211 [?]2119·211
(δz+1, δz2+δ, z4+δ){2,4,8}11211 [?]211
((δ+1)z+1, (δ+1)z2+(δ+1), z4+(δ+1)){2,4,8}11211 [?]211
(z+δ, z2+1, z4+1){2,4,8}11211 [?]211
(δz+δ, δz2+δ, z4+δ){2,4,8}11211 [?]211
((δ+1)z+δ, (δ+1)z2+(δ+1), z4+(δ+1)){2,4,8}11211 [?]211
(z+(δ+1), z2+1, z4+1){2,4,8}11211 [?]211
(δz+(δ+1), δz2+δ, z4+δ){2,4,8}11211 [?]211
((δ+1)z+(δ+1), (δ+1)z2+(δ+1), z4+(δ+1)){2,4,8}11211 [?]211
{(1,17), (2,10), (4,8), (8,0)}[ 7, 1, 2 ](z+1, z2+1, z4+1){2,4,8}13211 [?]2119·211
(δz+1, z2+δ, z4+1){2,4,8}13211 [?]211
((δ+1)z+1, z2+(δ+1), z4+1){2,4,8}13211 [?]211
(z+δ, z2+1, z4+1){2,4,8}13211 [?]211
(δz+δ, z2+δ, z4+1){2,4,8}13211 [?]211
((δ+1)z+δ, z2+(δ+1), z4+1){2,4,8}13211 [?]211
(z+(δ+1), z2+1, z4+1){2,4,8}13211 [?]211
(δz+(δ+1), z2+δ, z4+1){2,4,8}13211 [?]211
((δ+1)z+(δ+1), z2+(δ+1), z4+1){2,4,8}13211 [?]211
{(1,17), (2,14), (4,8), (8,0)}[ 3, 2 ](z3+z+1, z4+1){1}3127 [26]299·29
(z3+δz+1, z4+1){1}3127 [26]29
(z3+(δ+1)z+1, z4+1){1}3127 [26]29
(z3+z+δ, z4+1){2}2128 [27]29
(z3+δz+δ, z4+1){2}2128 [27]29
(z3+(δ+1)z+δ, z4+1){2}2128 [27]29
(z3+z+(δ+1), z4+1){2}2128 [27]29
(z3+δz+(δ+1), z4+1){2}2128 [27]29
(z3+(δ+1)z+(δ+1), z4+1){2}2128 [27]29
18{(1,18), (2,10), (4,4), (8,0)}[ 8, 3, 1 ](z+1, z2+1, z4+1){2,4,8}11213 [?]2139·2133·215
(z+1, δz2+1, z4+δ){2,4,8}11213 [?]213
(z+1, (δ+1)z2+1, z4+(δ+1)){2,4,8}11213 [?]213
(δz+δ, z2+δ, z4+1){2,4,8}11213 [?]213
(δz+δ, δz2+δ, z4+δ){2,4,8}11213 [?]213
(δz+δ, (δ+1)z2+δ, z4+(δ+1)){2,4,8}11213 [?]213
((δ+1)z+(δ+1), z2+(δ+1), z4+1){2,4,8}11213 [?]213
((δ+1)z+(δ+1), δz2+(δ+1), z4+δ){2,4,8}11213 [?]213
((δ+1)z+(δ+1), (δ+1)z2+(δ+1), z4+(δ+1)){2,4,8}11213 [?]213
{(1,18), (2,10), (4,8), (8,0)}[ 8, 1, 2 ](z+1, z2+1, z4+1){2,4,8}13213 [?]2133·213
(δz+δ, z2+δ, z4+1){2,4,8}13213 [?]213
((δ+1)z+(δ+1), z2+(δ+1), z4+1){2,4,8}13213 [?]213
19{(1,19), (2,12), (4,4), (8,0)}[ 7, 4, 1 ](z+1, z2+1, z4+1){2,4,8}11213 [?]2139·2133·215
(δz+1, δz2+δ, z4+δ){2,4,8}11213 [?]213
((δ+1)z+1, (δ+1)z2+(δ+1), z4+(δ+1)){2,4,8}11213 [?]213
(z+δ, z2+1, z4+1){2,4,8}11213 [?]213
(δz+δ, δz2+δ, z4+δ){2,4,8}11213 [?]213
((δ+1)z+δ, (δ+1)z2+(δ+1), z4+(δ+1)){2,4,8}11213 [?]213
(z+(δ+1), z2+1, z4+1){2,4,8}11213 [?]213
(δz+(δ+1), δz2+δ, z4+δ){2,4,8}11213 [?]213
((δ+1)z+(δ+1), (δ+1)z2+(δ+1), z4+(δ+1)){2,4,8}11213 [?]213
{(1,19), (2,14), (4,8), (8,0)}[ 5, 3, 2 ](z+1, z2+1, z4+1){2,4,8}11211 [?]2119·211
(δz+1, z2+δ, z4+1){2,4,8}11211 [?]211
((δ+1)z+1, z2+(δ+1), z4+1){2,4,8}11211 [?]211
(z+δ, z2+1, z4+1){2,4,8}11211 [?]211
(δz+δ, z2+δ, z4+1){2,4,8}11211 [?]211
((δ+1)z+δ, z2+(δ+1), z4+1){2,4,8}11211 [?]211
(z+(δ+1), z2+1, z4+1){2,4,8}11211 [?]211
(δz+(δ+1), z2+δ, z4+1){2,4,8}11211 [?]211
((δ+1)z+(δ+1), z2+(δ+1), z4+1){2,4,8}11211 [?]211
{(1,19), (2,16), (4,8), (8,0)}[ 3, 4, 2 ](z+1, z2+1, z4+1){1}13210 [28]2113·211
(z+δ, z2+1, z4+1){1}13210 [28]211
(z+(δ+1), z2+1, z4+1){1}13210 [28]211
20{(1,20), (2,12), (4,4), (8,0)}[ 8, 4, 1 ](z+1, z2+1, z4+1){2,4,8}11215 [?]2153·2153·215
(δz+δ, δz2+δ, z4+δ){2,4,8}11215 [?]215
((δ+1)z+(δ+1), (δ+1)z2+(δ+1), z4+(δ+1)){2,4,8}11215 [?]215
21{(1,21), (2,14), (4,8), (8,0)}[ 7, 3, 2 ](z+1, z2+1, z4+1){2,4,8}11213 [?]2139·2133·215
(δz+1, z2+δ, z4+1){2,4,8}11213 [?]213
((δ+1)z+1, z2+(δ+1), z4+1){2,4,8}11213 [?]213
(z+δ, z2+1, z4+1){2,4,8}11213 [?]213
(δz+δ, z2+δ, z4+1){2,4,8}11213 [?]213
((δ+1)z+δ, z2+(δ+1), z4+1){2,4,8}11213 [?]213
(z+(δ+1), z2+1, z4+1){2,4,8}11213 [?]213
(δz+(δ+1), z2+δ, z4+1){2,4,8}11213 [?]213
((δ+1)z+(δ+1), z2+(δ+1), z4+1){2,4,8}11213 [?]213
{(1,21), (2,16), (4,8), (8,0)}[ 5, 4, 2 ](z+1, z2+1, z4+1){2,4,8}11213 [?]2133·213
(z+δ, z2+1, z4+1){2,4,8}11213 [?]213
(z+(δ+1), z2+1, z4+1){2,4,8}11213 [?]213
22{(1,22), (2,14), (4,8), (8,0)}[ 8, 3, 2 ](z+1, z2+1, z4+1){2,4,8}11215 [?]2153·2153·215
(δz+δ, z2+δ, z4+1){2,4,8}11215 [?]215
((δ+1)z+(δ+1), z2+(δ+1), z4+1){2,4,8}11215 [?]215
23{(1,23), (2,16), (4,8), (8,0)}[ 7, 4, 2 ](z+1, z2+1, z4+1){2,4,8}11215 [?]2153·2153·215
(z+δ, z2+1, z4+1){2,4,8}11215 [?]215
(z+(δ+1), z2+1, z4+1){2,4,8}11215 [?]215
24{(1,24), (2,16), (4,8), (8,0)}[ 8, 4, 2 ](z+1, z2+1, z4+1){2,4,8}11217 [?]217217217