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Label Polynomial Discriminant Galois group Class group
7.7.1817487424.1 x7 - 8x5 - 2x4 + 16x3 + 6x2 - 6x - 2 \( 2^{6}\cdot 73^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.9597924961.1 x7 - x6 - 15x5 + 20x4 + 33x3 - 22x2 - 32x - 8 \( 313^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.18078415936.1 x7 - 14x5 + 56x3 - 56x - 22 \( 2^{6}\cdot 7^{10} \) $C_7:C_3$ (as 7T3) Trivial
7.7.100367308864.1 x7 - 2x6 - 14x5 + 4x4 + 30x3 + 8x2 - 6x - 2 \( 2^{6}\cdot 199^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.272225149504.1 x7 - 3x6 - 15x5 + 39x4 + 43x3 - 133x2 + 63x - 7 \( 2^{6}\cdot 7^{4}\cdot 11^{6} \) $C_7:C_3$ (as 7T3) Trivial
7.7.387790161984.1 x7 - 18x5 - 18x4 + 60x3 + 96x2 + 44x + 6 \( 2^{6}\cdot 3^{8}\cdot 31^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.525346636864.1 x7 - x6 - 25x5 + 49x4 + 131x3 - 415x2 + 281x + 7 \( 2^{6}\cdot 7^{4}\cdot 43^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.591559418641.1 x7 - 2x6 - 20x5 + 34x4 + 107x3 - 166x2 - 119x + 138 \( 877^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.1624709678881.1 x7 - x6 - 27x5 - 14x4 + 159x3 + 164x2 - 108x - 40 \( 1129^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.1688107729984.1 x7 - x6 - 25x5 + 15x4 + 181x3 - 37x2 - 311x - 121 \( 2^{6}\cdot 13^{4}\cdot 31^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.2420662999104.1 x7 - 42x5 - 56x4 + 126x3 + 168x2 - 98x - 126 \( 2^{6}\cdot 3^{8}\cdot 7^{8} \) $C_7:C_3$ (as 7T3) Trivial
7.7.2528484794641.1 x7 - 2x6 - 20x5 + 29x4 + 119x3 - 91x2 - 234x + 13 \( 13^{4}\cdot 97^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.5323914784321.1 x7 - 28x5 - 14x4 + 196x3 + 112x2 - 364x - 229 \( 7^{8}\cdot 31^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.5482378736704.1 x7 - x6 - 27x5 + 7x4 + 219x3 + 83x2 - 495x - 409 \( 2^{6}\cdot 541^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.6029426229121.1 x7 - 3x6 - 32x5 + 4x4 + 179x3 + 89x2 - 231x - 145 \( 1567^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.10537502807104.1 x7 - 28x5 - 28x4 + 182x3 + 238x2 - 266x - 374 \( 2^{6}\cdot 7^{8}\cdot 13^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.10804165206961.1 x7 - 35x5 - 70x4 + 84x3 + 196x2 - 49x - 134 \( 7^{8}\cdot 37^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.11239665258721.1 x7 - 2x6 - 45x5 + 23x4 + 679x3 + 384x2 - 3372x - 4399 \( 1831^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.13603763435584.1 x7 - 2x6 - 36x5 + 66x4 + 166x3 - 92x2 - 116x + 50 \( 2^{6}\cdot 7^{4}\cdot 97^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.15588038452561.1 x7 - x6 - 47x5 + 517x3 + 506x2 - 376x - 168 \( 1987^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.20161545805921.1 x7 - 3x6 - 38x5 + 52x4 + 351x3 - 168x2 - 321x - 17 \( 13^{4}\cdot 163^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.22747786847296.1 x7 - x6 - 39x5 + 75x4 + 55x3 - 123x2 + 19x + 9 \( 2^{6}\cdot 7^{4}\cdot 23^{6} \) $C_7:C_3$ (as 7T3) Trivial
7.7.24551549322304.1 x7 - 2x6 - 46x5 + 184x4 - 224x3 + 68x2 + 20x - 2 \( 2^{6}\cdot 787^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.26226371926561.1 x7 - x6 - 41x5 + 39x4 + 496x3 - 434x2 - 1643x + 961 \( 31^{4}\cdot 73^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.35271352782961.1 x7 - 3x6 - 54x5 + 27x4 + 809x3 + 1563x2 + 740x - 171 \( 2437^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.35698940069881.1 x7 - 3x6 - 59x5 + 83x4 + 791x3 - 507x2 - 2555x - 722 \( 11^{6}\cdot 67^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.42748699986001.1 x7 - 2x6 - 47x5 + 47x4 + 430x3 - 216x2 - 200x + 96 \( 2557^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.48081576391744.1 x7 - 70x5 - 42x4 + 1316x3 + 1428x2 - 2912x - 1940 \( 2^{6}\cdot 7^{8}\cdot 19^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.58280536320561.1 x7 - 3x6 - 36x5 + 143x4 + 204x3 - 1476x2 + 1800x - 432 \( 3^{8}\cdot 307^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.79818518042641.1 x7 - 56x5 - 42x4 + 777x3 + 1197x2 + 455x + 9 \( 7^{8}\cdot 61^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.90812685325761.1 x7 - 42x5 - 70x4 + 168x3 + 126x2 - 84x - 45 \( 3^{8}\cdot 7^{12} \) $C_7:C_3$ (as 7T3) Trivial
7.7.91402930798144.1 x7 - 2x6 - 48x5 - 60x4 + 100x3 + 132x2 + 4x - 12 \( 2^{6}\cdot 7^{4}\cdot 29^{6} \) $C_7:C_3$ (as 7T3) $[7]$
7.7.107103643129921.1 x7 - 2x6 - 43x5 + 9x4 + 527x3 + 614x2 - 488x - 248 \( 3217^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.156750600320064.1 x7 - 30x5 - 22x4 + 252x3 + 252x2 - 636x - 684 \( 2^{6}\cdot 3^{8}\cdot 139^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.162614549665681.1 x7 - x6 - 38x5 + 87x4 + 236x3 - 772x2 + 392x + 96 \( 3571^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.270595393646656.1 x7 - x6 - 39x5 - 17x4 + 331x3 + 291x2 - 441x - 83 \( 2^{6}\cdot 13^{4}\cdot 23^{6} \) $C_7:C_3$ (as 7T3) Trivial
7.7.316838611601521.1 x7 - x6 - 45x5 - 37x4 + 267x3 + 59x2 - 287x - 80 \( 4219^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.354452954340241.1 x7 - 2x6 - 64x5 + 271x4 + 326x3 - 3242x2 + 5176x - 2281 \( 4339^{4} \) $C_7:C_3$ (as 7T3) $[4]$
7.7.394259782912576.1 x7 - x6 - 63x5 + 89x4 + 1203x3 - 1951x2 - 7145x + 12679 \( 2^{6}\cdot 7^{4}\cdot 37^{6} \) $C_7:C_3$ (as 7T3) Trivial
7.7.500422134593689.1 x7 - 77x5 + 1694x3 - 9317x - 8228 \( 7^{10}\cdot 11^{6} \) $C_7:C_3$ (as 7T3) Trivial
7.7.523361201113921.1 x7 - 47x5 - 9x4 + 529x3 + 392x2 - 1115x - 1079 \( 4783^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.971365931561536.1 x7 - 3x6 - 33x5 + 85x4 + 25x3 - 117x2 + 29x + 7 \( 2^{6}\cdot 7^{4}\cdot 43^{6} \) $C_7:C_3$ (as 7T3) $[7]$
7.7.3405864388526656.1 x7 - x6 - 45x5 - 65x4 + 85x3 + 129x2 + 9x - 11 \( 2^{6}\cdot 7^{4}\cdot 53^{6} \) $C_7:C_3$ (as 7T3) $[2]$
7.7.3429038075724121.1 x7 - 203x5 - 406x4 + 9338x3 + 49126x2 + 70035x + 4408 \( 7^{8}\cdot 29^{6} \) $C_7:C_3$ (as 7T3) $[7]$
7.7.25300544239856704.1 x7 - 84x5 - 28x4 + 1456x3 + 1806x2 - 3906x - 5238 \( 2^{6}\cdot 7^{12}\cdot 13^{4} \) $C_7:C_3$ (as 7T3) Trivial
7.7.32027016613996096.1 x7 - 154x5 + 6776x3 - 74536x - 39930 \( 2^{6}\cdot 7^{10}\cdot 11^{6} \) $C_7:C_3$ (as 7T3) Trivial
7.7.32027016613996096.2 x7 - 154x5 + 6776x3 - 74536x - 77198 \( 2^{6}\cdot 7^{10}\cdot 11^{6} \) $C_7:C_3$ (as 7T3) Trivial
7.7.32027016613996096.3 x7 - 154x5 + 6776x3 - 74536x - 95832 \( 2^{6}\cdot 7^{10}\cdot 11^{6} \) $C_7:C_3$ (as 7T3) Trivial
7.7.32027016613996096.4 x7 - 154x5 + 6776x3 - 74536x - 96360 \( 2^{6}\cdot 7^{10}\cdot 11^{6} \) $C_7:C_3$ (as 7T3) Trivial
7.7.32027016613996096.5 x7 - 154x5 + 6776x3 - 74536x - 99220 \( 2^{6}\cdot 7^{10}\cdot 11^{6} \) $C_7:C_3$ (as 7T3) Trivial
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