Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
14.0.9095120158391.1 |
x14 - 7x13 + 25x12 - 59x11 + 103x10 - 141x9 + 159x8 - 153x7 + 129x6 - 95x5 + 58x4 - 27x3 + 10x2 - 3x + 1 |
$14$ |
[0,7] |
$-\,71^{7}$ |
$$ |
$8.42614977318$ |
|
✓ |
not computed |
$D_{7}$ (as 14T2) |
trivial |
$2$ |
$6$ |
$2.56161916129$ |
14.0.9669040949311.1 |
x14 - x13 + 3x12 - 6x11 + 5x10 - 9x9 + 11x8 - 7x7 + 11x6 - 9x5 + 5x4 - 6x3 + 3x2 - x + 1 |
$14$ |
[0,7] |
$-\,19^{2}\cdot 79\cdot 18413^{2}$ |
$$ |
$8.46305933364$ |
|
|
✓ |
14T57 |
trivial |
$2$ |
$6$ |
$2.65828702774$ |
14.0.9745585291264.1 |
x14 - 4x13 + 7x12 - 4x11 - 8x10 + 24x9 - 30x8 + 16x7 + 13x6 - 38x5 + 46x4 - 36x3 + 19x2 - 6x + 1 |
$14$ |
[0,7] |
$-\,2^{14}\cdot 29^{6}$ |
$$ |
$8.467827352511435$ |
|
|
✓ |
$C_7 \wr C_2$ (as 14T8) |
trivial |
$4$ |
$6$ |
$5.342840135225723$ |
14.0.9866941650479.1 |
x14 - 3x13 + 6x12 - 11x11 + 16x10 - 21x9 + 25x8 - 25x7 + 25x6 - 21x5 + 16x4 - 11x3 + 6x2 - 3x + 1 |
$14$ |
[0,7] |
$-\,167^{2}\cdot 191\cdot 1361^{2}$ |
$$ |
$8.47531594932$ |
|
|
✓ |
14T57 |
trivial |
$2$ |
$6$ |
$2.68866215877$ |
14.0.11856232199187.1 |
x14 - x13 + x12 - x10 - x9 + x8 - x7 - x6 + 3x5 - 2x4 + x3 + x2 - x + 1 |
$14$ |
[0,7] |
$-\,3^{7}\cdot 5421231001$ |
$$ |
$8.58723475068$ |
|
|
✓ |
14T61 |
trivial |
$6$ |
$6$ |
$9.0466002324$ |
14.0.12985240103739.1 |
x14 - x13 + x12 - 4x11 + 4x10 - 2x9 + 5x8 - 6x7 + 2x6 - 2x5 + 5x4 - 2x3 - x + 1 |
$14$ |
[0,7] |
$-\,3^{7}\cdot 5937466897$ |
$$ |
$8.64320868463$ |
|
|
✓ |
14T61 |
trivial |
$6$ |
$6$ |
$9.5585171283$ |
14.0.13048447346663.1 |
x14 - x13 + 2x12 - 2x11 + 2x10 - 2x9 + x8 - x7 + x6 - 2x5 + 2x4 - 2x3 + 2x2 - x + 1 |
$14$ |
[0,7] |
$-\,23\cdot 37^{2}\cdot 20357^{2}$ |
$$ |
$8.64620704819$ |
|
|
✓ |
14T57 |
trivial |
$2$ |
$6$ |
$3.18798462168$ |
14.0.13824820988163.1 |
x14 - 3x13 + 8x12 - 18x11 + 32x10 - 52x9 + 70x8 - 81x7 + 82x6 - 70x5 + 52x4 - 31x3 + 16x2 - 6x + 1 |
$14$ |
[0,7] |
$-\,3^{7}\cdot 43^{6}$ |
$$ |
$8.681975119007818$ |
|
|
not computed |
$C_7 \wr C_2$ (as 14T8) |
trivial |
$6$ |
$6$ |
$9.923787361493524$ |
14.0.16973485041483.1 |
x14 - 2x13 + 2x12 - 6x11 + 8x10 - 4x9 + 9x8 - 11x7 + 6x6 - 6x5 + 5x4 - 4x3 + 2x2 + 1 |
$14$ |
[0,7] |
$-\,3^{7}\cdot 37^{2}\cdot 2381^{2}$ |
$$ |
$8.81015693246$ |
|
|
not computed |
$S_7\times C_2$ (as 14T49) |
trivial |
$6$ |
$6$ |
$11.1445691239$ |
14.0.22139206005899.1 |
x14 - 3x13 + 4x12 - 2x11 + x10 - 4x9 + 9x8 - 11x7 + 9x6 - 4x5 + x4 - 2x3 + 4x2 - 3x + 1 |
$14$ |
[0,7] |
$-\,59\cdot 593^{2}\cdot 1033^{2}$ |
$$ |
$8.97895634588$ |
|
|
✓ |
14T57 |
trivial |
$2$ |
$6$ |
$4.38657959616$ |
14.0.28466647927227.1 |
x14 - x13 + 2x12 + 3x11 - x10 + 4x9 + 3x8 + 2x7 + 2x4 - 2x3 - x2 + 1 |
$14$ |
[0,7] |
$-\,3^{7}\cdot 114089^{2}$ |
$$ |
$9.14163808258$ |
|
|
not computed |
$S_7\times C_2$ (as 14T49) |
trivial |
$6$ |
$6$ |
$15.4833298742$ |
14.0.30270895108587.1 |
x14 - 4x13 + 6x12 - 3x11 - 6x10 + 14x9 - 12x8 + 2x7 + 10x6 - 8x5 - 3x4 + x3 + 7x2 - 5x + 1 |
$14$ |
[0,7] |
$-\,3^{7}\cdot 7^{12}$ |
$$ |
$9.181853855048184$ |
|
|
not computed |
$C_7 \wr C_2$ (as 14T8) |
trivial |
$6$ |
$6$ |
$16.520791850817314$ |
14.0.51902598731283.1 |
x14 - 2x13 + 3x12 - 6x11 + 6x10 - 4x9 + 3x8 + x7 - x5 + 3x4 + 3x2 + x + 1 |
$14$ |
[0,7] |
$-\,3^{11}\cdot 17117^{2}$ |
$$ |
$9.54237247067$ |
|
|
not computed |
$S_7\times C_2$ (as 14T49) |
trivial |
$6$ |
$6$ |
$27.6082700412$ |
14.2.52058057626129.1 |
x14 - 2x13 + 3x12 - 4x11 + 4x10 - 4x9 + 4x8 - 5x7 + 4x6 - 4x5 + 4x4 - 4x3 + 3x2 - 2x + 1 |
$14$ |
[2,6] |
$7215127^{2}$ |
$$ |
$9.54441116258$ |
|
|
not computed |
14T55 |
trivial |
$2$ |
$7$ |
$9.48144292717$ |
14.2.54815765790289.1 |
x14 + x12 - 2x8 - x7 - 2x6 + x2 + 1 |
$14$ |
[2,6] |
$7^{2}\cdot 1057681^{2}$ |
$$ |
$9.57966653808$ |
|
|
✓ |
14T55 |
trivial |
$2$ |
$7$ |
$9.77968117968$ |
14.2.55059380046329.1 |
x14 - 4x13 + 6x12 - x11 - 10x10 + 18x9 - 18x8 + 15x7 - 13x6 + 11x5 - 8x4 + 6x3 - 3x2 + 1 |
$14$ |
[2,6] |
$277^{2}\cdot 569\cdot 1123^{2}$ |
$$ |
$9.58270130317$ |
|
|
not computed |
14T57 |
trivial |
$2$ |
$7$ |
$9.77909350979$ |
14.0.56316949686099.1 |
x14 - 2x13 + 6x12 - 11x11 + 19x10 - 26x9 + 33x8 - 35x7 + 33x6 - 26x5 + 19x4 - 10x3 + 6x2 - x + 1 |
$14$ |
[0,7] |
$-\,3^{7}\cdot 2953^{3}$ |
$$ |
$9.59817157113$ |
|
|
✓ |
$D_7 \wr C_2$ (as 14T20) |
trivial |
$6$ |
$6$ |
$24.3506832156$ |
14.2.62662828387597.1 |
x14 - x13 - 3x12 + 5x11 + 2x10 - 11x9 + 4x8 + 11x7 - 11x6 - 2x5 + 10x4 - 4x3 - 2x2 + 3x - 1 |
$14$ |
[2,6] |
$167^{2}\cdot 1213\cdot 1361^{2}$ |
$$ |
$9.67165316326$ |
|
|
✓ |
14T57 |
trivial |
$2$ |
$7$ |
$10.6313575761$ |
14.2.63097400703125.1 |
x14 - 3x13 + 2x12 + 4x11 - 8x10 + 2x9 + 8x8 - 10x7 + x6 + 7x5 - 6x4 + x3 + 2x2 - x + 1 |
$14$ |
[2,6] |
$5^{7}\cdot 807646729$ |
$$ |
$9.6764287896$ |
|
|
not computed |
14T61 |
trivial |
$2$ |
$7$ |
$10.6889300961$ |
14.2.68537510017457.1 |
x14 - 4x13 + 10x12 - 15x11 + 11x10 + 6x9 - 26x8 + 35x7 - 26x6 + 6x5 + 11x4 - 15x3 + 10x2 - 4x + 1 |
$14$ |
[2,6] |
$13^{4}\cdot 17\cdot 109^{4}$ |
$$ |
$9.73375911642$ |
|
|
✓ |
14T51 |
trivial |
$2$ |
$7$ |
$11.2548274629$ |
14.0.74532401109963.1 |
x14 - x13 + 2x12 - x11 + 2x10 - 2x9 + 2x8 - 2x7 - 3x5 - x3 + 2x2 + x + 1 |
$14$ |
[0,7] |
$-\,3^{7}\cdot 184607^{2}$ |
$$ |
$9.79223424158$ |
|
|
not computed |
$S_7\times C_2$ (as 14T49) |
trivial |
$6$ |
$6$ |
$26.6828967522$ |
14.0.76600746490099.1 |
x14 - 2x13 + 6x12 - 8x11 + 16x10 - 17x9 + 24x8 - 21x7 + 24x6 - 17x5 + 16x4 - 8x3 + 6x2 - 2x + 1 |
$14$ |
[0,7] |
$-\,13^{4}\cdot 19\cdot 109^{4}$ |
$$ |
$9.811398801$ |
|
|
not computed |
14T51 |
trivial |
$2$ |
$6$ |
$9.51678072789$ |
14.2.78352380449344.1 |
x14 - 2x12 + x10 + 2x8 - 3x6 + x4 - 1 |
$14$ |
[2,6] |
$2^{6}\cdot 23^{2}\cdot 73^{2}\cdot 659^{2}$ |
$$ |
$9.82725668122$ |
|
|
not computed |
14T55 |
trivial |
$2$ |
$7$ |
$12.5841466704$ |
14.2.94241555580481.1 |
x14 - x12 - 2x9 + 3x7 - 2x5 - x2 + 1 |
$14$ |
[2,6] |
$43^{2}\cdot 401^{2}\cdot 563^{2}$ |
$$ |
$9.95772606431$ |
|
|
✓ |
14T55 |
trivial |
$2$ |
$7$ |
$13.4715273772$ |
14.2.94724481953125.1 |
x14 - x13 - 2x12 + 5x11 + 2x10 - 9x9 + 2x8 + 10x7 - 6x6 - 6x5 + 7x4 + x3 - 4x2 + 1 |
$14$ |
[2,6] |
$5^{7}\cdot 199\cdot 6092831$ |
$$ |
$9.96136219536$ |
|
|
✓ |
14T61 |
trivial |
$2$ |
$7$ |
$13.5893961295$ |
14.2.103886084489093.1 |
x14 - 3x12 - 3x11 + 6x10 + 7x9 - 5x8 - 12x7 + 2x6 + 11x5 + x4 - 7x3 - 2x2 + 4x - 1 |
$14$ |
[2,6] |
$53\cdot 977^{2}\cdot 1433^{2}$ |
$$ |
$10.0272690923$ |
|
|
not computed |
14T57 |
trivial |
$2$ |
$7$ |
$14.647522546$ |
14.2.116768679686993.1 |
x14 - 3x13 + 7x12 - 14x11 + 21x10 - 29x9 + 35x8 - 37x7 + 35x6 - 29x5 + 21x4 - 14x3 + 7x2 - 3x + 1 |
$14$ |
[2,6] |
$257\cdot 674057^{2}$ |
$$ |
$10.1113472722$ |
|
|
✓ |
14T57 |
trivial |
$2$ |
$7$ |
$15.418973911$ |
14.0.118236562059083.1 |
x14 - 3x13 + 2x12 + 3x11 - 5x10 - x9 + x8 + 2x7 + 11x6 - 13x5 + 6x4 - 8x3 + 4x2 + 1 |
$14$ |
[0,7] |
$-\,13\cdot 71^{7}$ |
$$ |
$10.1203738706$ |
|
|
not computed |
14T38 |
trivial |
$2$ |
$6$ |
$12.9746502268$ |
14.2.154291569457229.1 |
x14 - x13 + x12 - 2x11 + 2x10 - 3x9 + 3x8 - 3x7 + 3x6 - 3x5 + 2x4 - 2x3 + x2 - x + 1 |
$14$ |
[2,6] |
$29\cdot 107^{2}\cdot 21557^{2}$ |
$$ |
$10.3146148047$ |
|
|
✓ |
14T57 |
trivial |
$2$ |
$7$ |
$17.8336574914$ |
14.2.160805685121205.1 |
x14 + x12 - x9 - x8 - x7 - x6 - x5 + x2 + 1 |
$14$ |
[2,6] |
$5\cdot 41^{2}\cdot 138319^{2}$ |
$$ |
$10.3451267052$ |
|
|
✓ |
14T57 |
trivial |
$2$ |
$7$ |
$20.4518453354$ |
14.0.172575877556547.1 |
x14 - x13 - x12 + 2x10 + x9 - x8 - x7 - x6 + x5 + 2x4 - x2 - x + 1 |
$14$ |
[0,7] |
$-\,3^{7}\cdot 280909^{2}$ |
$$ |
$10.3974573916$ |
|
|
✓ |
$S_7\times C_2$ (as 14T49) |
trivial |
$6$ |
$6$ |
$55.4764206676$ |
14.2.212764932023296.1 |
x14 - x10 + x8 + x2 - 1 |
$14$ |
[2,6] |
$2^{10}\cdot 455827^{2}$ |
$$ |
$10.5541055231$ |
|
|
not computed |
14T55 |
trivial |
$2$ |
$7$ |
$21.4724068698$ |
14.2.245928712415581.1 |
x14 - x13 + 4x12 - x11 + 3x10 + 3x9 - 4x8 + 9x7 - 16x6 + 14x5 - 21x4 + 10x3 - 9x2 + 2x - 1 |
$14$ |
[2,6] |
$13^{4}\cdot 61\cdot 109^{4}$ |
$$ |
$10.6638725375$ |
|
|
not computed |
14T51 |
trivial |
$2$ |
$7$ |
$26.4300628611$ |
14.4.250058750499647.1 |
x14 - 2x13 + x12 - x11 + x10 - 4x9 + 9x8 - 9x7 + 9x6 - 4x5 + x4 - x3 + x2 - 2x + 1 |
$14$ |
[4,5] |
$-\,47\cdot 107^{2}\cdot 21557^{2}$ |
$$ |
$10.676565665$ |
|
|
✓ |
14T57 |
trivial |
$2$ |
$8$ |
$31.5102502485$ |
14.0.263657868936003.1 |
x14 + x12 - 2x11 - x10 + 3x7 - x4 - 2x3 + x2 + 1 |
$14$ |
[0,7] |
$-\,3^{7}\cdot 103^{2}\cdot 3371^{2}$ |
$$ |
$10.717027334$ |
|
|
✓ |
$S_7\times C_2$ (as 14T49) |
trivial |
$6$ |
$6$ |
$73.5044803741$ |
14.4.270118421833507.1 |
x14 - x13 - 3x12 - x11 + x10 + 2x8 + 7x7 + 3x6 + 4x5 + 9x4 + 7x3 + x2 + 1 |
$14$ |
[4,5] |
$-\,13^{4}\cdot 67\cdot 109^{4}$ |
$$ |
$10.7355747516$ |
|
|
not computed |
14T51 |
trivial |
$2$ |
$8$ |
$33.079338429$ |
14.0.280155320935227.1 |
x14 - x13 + 2x12 - x11 + 3x10 - 4x9 + 3x8 - 4x7 + 2x6 - 4x5 + 2x4 + 5x2 + 2x + 1 |
$14$ |
[0,7] |
$-\,3^{7}\cdot 71^{6}$ |
$$ |
$10.763587918$ |
|
|
not computed |
$D_{14}$ (as 14T3) |
trivial |
$6$ |
$6$ |
$64.9438034848$ |
14.4.297261105546875.1 |
x14 - 3x12 - x11 + 5x10 + 3x9 - 6x8 - 6x7 + 3x6 + 7x5 - 4x3 - 2x2 + x + 1 |
$14$ |
[4,5] |
$-\,5^{7}\cdot 89\cdot 971\cdot 44029$ |
$$ |
$10.8092504055$ |
|
|
✓ |
14T61 |
trivial |
$2$ |
$8$ |
$34.9413880804$ |
14.0.318497840669359.1 |
x14 - 4x13 + 8x12 - 10x11 + 15x10 - 28x9 + 42x8 - 41x7 + 32x6 - 31x5 + 37x4 - 35x3 + 21x2 - 7x + 1 |
$14$ |
[0,7] |
$-\,13^{4}\cdot 79\cdot 109^{4}$ |
$$ |
$10.8626597908$ |
|
|
not computed |
14T51 |
trivial |
$2$ |
$6$ |
$22.560872956$ |
14.2.321952970703125.1 |
x14 - 3x13 + 2x12 + 3x11 - 7x10 + 11x9 - 25x8 + 33x7 - 4x6 - 56x5 + 93x4 - 78x3 + 38x2 - 10x + 1 |
$14$ |
[2,6] |
$5^{9}\cdot 37^{2}\cdot 347^{2}$ |
$$ |
$10.8710348587$ |
|
|
not computed |
$S_7\times C_2$ (as 14T49) |
trivial |
$2$ |
$7$ |
$30.836203822$ |
14.4.334624313614643.1 |
x14 - x13 - 4x12 + 3x11 + 3x10 + 3x9 + 2x8 - 12x7 + x5 + 2x4 + 6x3 - 3x2 + x - 1 |
$14$ |
[4,5] |
$-\,13^{4}\cdot 83\cdot 109^{4}$ |
$$ |
$10.9010515249$ |
|
|
not computed |
14T51 |
trivial |
$2$ |
$8$ |
$37.8345982696$ |
14.2.386441371953125.1 |
x14 - x13 - 2x12 + 4x11 - 2x10 - 3x9 + x8 + 6x6 - 11x5 + 5x4 - 12x3 + 24x2 - 20x + 5 |
$14$ |
[2,6] |
$5^{7}\cdot 53^{2}\cdot 1327^{2}$ |
$$ |
$11.0137330011$ |
|
|
not computed |
$S_7\times C_2$ (as 14T49) |
trivial |
$2$ |
$7$ |
$38.0258403894$ |
14.2.391066968923137.1 |
x14 - 4x13 + 5x12 + 4x11 - 14x10 + 5x9 + 13x8 - 9x7 - 9x6 + 8x5 + 4x4 - 5x3 + x - 1 |
$14$ |
[2,6] |
$13^{4}\cdot 97\cdot 109^{4}$ |
$$ |
$11.0230975946$ |
|
|
not computed |
14T51 |
trivial |
$2$ |
$7$ |
$35.8148412318$ |
14.0.407483719072587.1 |
x14 - x13 + 4x12 - x11 + 4x10 + 2x9 - 6x8 + 3x7 - 6x6 + 2x5 + 4x4 - x3 + 4x2 - x + 1 |
$14$ |
[0,7] |
$-\,3^{15}\cdot 73^{4}$ |
$$ |
$11.0555233042$ |
|
|
not computed |
$A_7\times C_2$ (as 14T47) |
trivial |
$6$ |
$6$ |
$96.5294199023$ |
14.4.411650990546875.1 |
x14 - 3x12 - 2x11 + 5x10 + 4x9 - 6x8 - 7x7 + 7x6 + 9x5 - 4x4 - 6x3 + 2x2 + 2x - 1 |
$14$ |
[4,5] |
$-\,5^{7}\cdot 24851\cdot 212029$ |
$$ |
$11.0635611432$ |
|
|
not computed |
14T61 |
trivial |
$2$ |
$8$ |
$42.0905477867$ |
14.2.422859037223221.1 |
x14 - 2x13 - 4x12 + 6x11 + 10x10 - 3x9 - 19x8 - 6x7 + 27x6 - x5 - 20x4 + 9x3 + 4x2 - 4x + 1 |
$14$ |
[2,6] |
$71^{6}\cdot 3301$ |
$$ |
$11.0848101244$ |
|
|
not computed |
14T38 |
trivial |
$2$ |
$7$ |
$32.6924434913$ |
14.0.445660887761159.1 |
x14 - x13 + 6x12 - 4x11 + 12x10 - 2x9 + 11x8 + 3x7 + 11x6 - 2x5 + 12x4 - 4x3 + 6x2 - x + 1 |
$14$ |
[0,7] |
$-\,7^{2}\cdot 71^{7}$ |
$$ |
$11.1264716525$ |
|
|
not computed |
14T27 |
trivial |
$2$ |
$6$ |
$25.684570553$ |
14.0.489862582246303.1 |
x14 - 5x13 + 18x12 - 44x11 + 89x10 - 140x9 + 190x8 - 209x7 + 201x6 - 156x5 + 104x4 - 55x3 + 23x2 - 7x + 1 |
$14$ |
[0,7] |
$-\,7^{7}\cdot 29^{6}$ |
$$ |
$11.201882659887865$ |
|
|
not computed |
$C_7 \wr C_2$ (as 14T8) |
trivial |
$2$ |
$6$ |
$30.78649932175806$ |
14.2.493856488203125.1 |
x14 - 2x13 + 6x11 - 3x10 - 8x9 + 13x8 + 4x7 - 16x6 + 7x5 + 13x4 - 11x3 - 4x2 + 6x - 1 |
$14$ |
[2,6] |
$5^{7}\cdot 43^{6}$ |
$$ |
$11.2083816827$ |
|
|
not computed |
$D_{14}$ (as 14T3) |
trivial |
$2$ |
$7$ |
$39.9535247267$ |
14.4.498897726810659.1 |
x14 - 2x13 + 3x11 - 7x10 + x9 + 14x8 - 2x7 - 13x6 + 2x5 + 4x4 - 4x3 + 3x + 1 |
$14$ |
[4,5] |
$-\,11^{3}\cdot 71^{2}\cdot 8623^{2}$ |
$$ |
$11.2165156356$ |
|
|
not computed |
14T57 |
trivial |
$2$ |
$8$ |
$47.3515916708$ |