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Results (displaying all 29 matches)

Label Polynomial Discriminant Galois group Class group
18.2.390877006486250192896.1 x18 + 7x16 + 18x14 + 19x12 + x10 - 19x8 - 27x6 - 22x4 - 8x2 - 1 \( 2^{24}\cdot 13^{12} \) 18T463 Trivial
18.2.10834375376002294480896.2 x18 + 4x16 + 11x14 + 19x12 + 25x10 + 20x8 + 8x6 - x4 - 3x2 - 1 \( 2^{30}\cdot 3^{6}\cdot 7^{12} \) 18T463 Trivial
18.10.19634130432842855035456.1 x18 - 9x16 - 8x15 + 24x14 + 41x13 - 21x12 - 91x11 - 14x10 + 151x9 + 112x8 - 119x7 - 161x6 + 5x5 + 79x4 + 27x3 - 10x2 - 7x - 1 \( 2^{6}\cdot 7^{12}\cdot 53^{6} \) 18T463 Trivial
18.6.1256584347701942722269184.2 x18 + 3x16 - 16x14 - 50x12 + 3x10 + 104x8 + 80x6 + 7x4 - 6x2 - 1 \( 2^{12}\cdot 7^{12}\cdot 53^{6} \) 18T463 Trivial
18.6.1256584347701942722269184.3 x18 + 10x16 + 31x14 + 17x12 - 59x10 - 54x8 + 27x6 + 27x4 - 1 \( 2^{12}\cdot 7^{12}\cdot 53^{6} \) 18T463 Trivial
18.10.1256584347701942722269184.4 x18 - 2x16 - 35x14 + 3x12 + 148x10 + 46x8 - 96x6 - 18x4 + 18x2 - 1 \( 2^{12}\cdot 7^{12}\cdot 53^{6} \) 18T463 Trivial
18.10.1256584347701942722269184.5 x18 - 3x16 - 12x14 + 17x12 + 28x10 - 23x8 - 22x6 + 9x4 + 5x2 - 1 \( 2^{12}\cdot 7^{12}\cdot 53^{6} \) 18T463 Trivial (GRH)
18.6.1592822467387587324542976.3 x18 - 9x16 - 16x15 + 13x14 + 72x13 + 62x12 - 70x11 - 50x10 + 218x9 + 339x8 + 188x7 - 1315x6 + 958x5 + 1519x4 - 2452x3 + 860x2 - 96x + 1 \( 2^{24}\cdot 3^{6}\cdot 7^{12}\cdot 97^{2} \) 18T463 Trivial
18.6.1592822467387587324542976.4 x18 + x16 - 30x15 - 51x14 - 18x13 + 220x12 + 642x11 + 96x10 - 1456x9 - 2043x8 - 480x7 + 2699x6 + 4290x5 + 2523x4 + 520x3 - 4x2 - 24x + 1 \( 2^{24}\cdot 3^{6}\cdot 7^{12}\cdot 97^{2} \) 18T463 Trivial
18.14.2886523956915912859821961.1 x18 - 3x17 - 15x16 + 46x15 + 74x14 - 231x13 - 192x12 + 540x11 + 331x10 - 667x9 - 403x8 + 457x7 + 333x6 - 147x5 - 160x4 - 4x3 + 30x2 + 10x + 1 \( 7^{12}\cdot 53^{6}\cdot 97^{2} \) 18T463 Trivial (GRH)
18.2.2886523956915912859821961.1 x18 + 2x16 - 3x15 - 4x14 - 4x13 - 6x12 - 4x10 - 17x9 - 8x8 - 48x6 - 64x5 - 128x4 - 192x3 + 256x2 + 512 \( 7^{12}\cdot 53^{6}\cdot 97^{2} \) 18T463 $[2]$
18.14.2886523956915912859821961.2 x18 - x17 - 15x16 + 4x15 + 92x14 + 35x13 - 280x12 - 255x11 + 411x10 + 603x9 - 209x8 - 649x7 - 93x6 + 331x5 + 126x4 - 70x3 - 34x2 + 3x + 1 \( 7^{12}\cdot 53^{6}\cdot 97^{2} \) 18T463 Trivial (GRH)
18.6.2886523956915912859821961.2 x18 - x17 - 6x16 + x14 + 23x13 + 13x12 + 24x11 - 9x10 + 5x9 - 9x8 + 24x7 + 13x6 + 23x5 + x4 - 6x2 - x + 1 \( 7^{12}\cdot 53^{6}\cdot 97^{2} \) 18T463 Trivial
18.2.80421398252924334225227776.1 x18 + 10x16 + 21x14 - 67x12 - 362x10 - 621x8 - 495x6 - 183x4 - 26x2 - 1 \( 2^{18}\cdot 7^{12}\cdot 53^{6} \) 18T463 $[6]$
18.14.80421398252924334225227776.3 x18 - x16 - 22x14 + 62x12 - 8x10 - 144x8 + 185x6 - 91x4 + 18x2 - 1 \( 2^{18}\cdot 7^{12}\cdot 53^{6} \) 18T463 Trivial (GRH)
18.14.80421398252924334225227776.4 x18 - 13x16 + 65x14 - 146x12 + 87x10 + 240x8 - 507x6 + 362x4 - 87x2 - 1 \( 2^{18}\cdot 7^{12}\cdot 53^{6} \) 18T463 Trivial (GRH)
18.10.80421398252924334225227776.5 x18 + x16 - 16x14 - 4x12 + 89x10 - 40x8 - 158x6 + 169x4 - 42x2 - 1 \( 2^{18}\cdot 7^{12}\cdot 53^{6} \) 18T463 Trivial (GRH)
18.10.80421398252924334225227776.6 x18 - 8x16 + 5x14 + 73x12 - 62x10 - 223x8 + 13x6 + 75x4 - 1 \( 2^{18}\cdot 7^{12}\cdot 53^{6} \) 18T463 Trivial (GRH)
18.6.80421398252924334225227776.6 x18 + 6x16 - 3x14 - 62x12 - 60x10 + 119x8 + 218x6 + 106x4 + 13x2 - 1 \( 2^{18}\cdot 7^{12}\cdot 53^{6} \) 18T463 Trivial
18.10.80421398252924334225227776.7 x18 + 5x16 - 12x14 - 50x12 + 53x10 + 83x8 - 96x6 + 5x4 + 13x2 - 1 \( 2^{18}\cdot 7^{12}\cdot 53^{6} \) 18T463 Trivial (GRH)
18.10.80421398252924334225227776.8 x18 - 8x16 + 6x14 + 62x12 - 64x10 - 130x8 + 31x6 + 77x4 + 18x2 - 1 \( 2^{18}\cdot 7^{12}\cdot 53^{6} \) 18T463 Trivial (GRH)
18.10.80421398252924334225227776.9 x18 - 5x16 - 3x14 + 38x12 - 21x10 - 53x8 + 20x6 + 29x4 + 3x2 - 1 \( 2^{18}\cdot 7^{12}\cdot 53^{6} \) 18T463 Trivial (GRH)
18.6.588359120644241989354055194546176.1 x18 + 27x16 + 225x14 + 222x12 - 5247x10 - 18486x8 + 16815x6 + 129960x4 + 61731x2 - 130321 \( 2^{12}\cdot 3^{32}\cdot 19^{4}\cdot 29^{6} \) 18T463 $[2]$ (GRH)
18.6.2566305730477550731264000000000000.1 x18 + 3x16 - 288x14 - 2589x12 + 4145x10 + 112601x8 + 334167x6 - 53824x4 - 1073116x2 - 707281 \( 2^{30}\cdot 5^{12}\cdot 7^{12}\cdot 29^{4} \) 18T463 $[2, 2]$ (GRH)
18.18.37196621191331827761794933720088576.1 x18 - 99x16 + 3771x14 - 72752x12 + 790428x10 - 5062413x8 + 19353109x6 - 43145919x4 + 51539184x2 - 25411681 \( 2^{30}\cdot 3^{24}\cdot 13^{6}\cdot 71^{4} \) 18T463 Trivial (GRH)
18.18.37196621191331827761794933720088576.2 x18 - 84x16 + 2961x14 - 56915x12 + 649875x10 - 4514730x8 + 18844962x6 - 44960679x4 + 54760383x2 - 25411681 \( 2^{30}\cdot 3^{24}\cdot 13^{6}\cdot 71^{4} \) 18T463 Trivial (GRH)
18.6.37654983721231487318659532450955264.2 x18 + 27x16 + 135x14 - 1641x12 - 14940x10 - 3537x8 + 252282x6 + 675792x4 + 370386x2 - 130321 \( 2^{18}\cdot 3^{32}\cdot 19^{4}\cdot 29^{6} \) 18T463 $[2]$ (GRH)
18.6.164243566750563246800896000000000000.1 x18 + 17x16 - 85x14 - 2463x12 - 3079x10 + 93715x8 + 275906x6 - 736716x4 - 2609623x2 - 707281 \( 2^{36}\cdot 5^{12}\cdot 7^{12}\cdot 29^{4} \) 18T463 $[2, 2]$ (GRH)
18.10.124103452202961465725793344698621400682587896362984419066163822801977344.1 x18 - 6x17 - 1186x16 + 2535x15 - 70915081x14 + 304399221x13 + 62447385363x12 - 367485308357x11 + 1298486657446163x10 - 3910634890096303x9 - 1073268117936735198x8 + 3439078251571123287x7 - 3447917848391399824309x6 + 6462730573786176922302x5 + 1840910048517668601690747x4 - 3345773125455451750808938x3 - 96033970663082701749723147x2 + 408195892123775028048902443x - 5894493332285389666473057161 \( 2^{18}\cdot 7^{12}\cdot 41^{4}\cdot 73^{12}\cdot 4794733^{4} \) 18T463 n/a


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