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Results (displaying all 16 matches)

Label Polynomial Discriminant Galois group Class group
16.0.73509189062500000000.1 x16 - 3x15 - 3x14 - 4x13 + 66x12 + 2x11 - 240x10 - 57x9 + 524x8 + 109x7 - 415x6 - 311x5 + 126x4 + 183x3 + 78x2 + 14x + 1 \( 2^{8}\cdot 5^{14}\cdot 19^{6} \) $(C_2\times Q_8).C_2^3$ (as 16T226) $[2]$
16.0.419430400000000000000.7 x16 - 10x14 + 30x12 - 20x10 + 60x8 - 200x6 - 200x4 + 400x2 + 400 \( 2^{36}\cdot 5^{14} \) $(C_2\times Q_8).C_2^3$ (as 16T226) Trivial (GRH)
16.4.6710886400000000000000.2 x16 - 20x12 - 30x10 + 95x8 + 150x6 - 50x4 - 50x2 + 25 \( 2^{40}\cdot 5^{14} \) $(C_2\times Q_8).C_2^3$ (as 16T226) Trivial (GRH)
16.4.26536817251562500000000.1 x16 - 3x15 + 2x14 - 4x13 - 24x12 + 7x11 - 40x10 - 37x9 + 14x8 + 109x7 + 170x6 + 469x5 + 671x4 + 443x3 + 28x2 - 96x - 29 \( 2^{8}\cdot 5^{14}\cdot 19^{8} \) $(C_2\times Q_8).C_2^3$ (as 16T226) $[2]$ (GRH)
16.8.8680963974111420152283136.3 x16 - 32x12 + 220x8 - 384x4 + 196 \( 2^{66}\cdot 7^{6} \) $(C_2\times Q_8).C_2^3$ (as 16T226) Trivial (GRH)
16.0.8680963974111420152283136.4 x16 + 4x12 + 26x8 + 44x4 + 49 \( 2^{66}\cdot 7^{6} \) $(C_2\times Q_8).C_2^3$ (as 16T226) $[2]$ (GRH)
16.8.8680963974111420152283136.4 x16 - 48x12 + 412x8 - 992x4 + 196 \( 2^{66}\cdot 7^{6} \) $(C_2\times Q_8).C_2^3$ (as 16T226) Trivial (GRH)
16.0.8680963974111420152283136.5 x16 + 12x12 + 90x8 + 36x4 + 49 \( 2^{66}\cdot 7^{6} \) $(C_2\times Q_8).C_2^3$ (as 16T226) $[2]$ (GRH)
16.0.12476445670501562500000000.1 x16 - x15 + 28x14 - 22x13 + 406x12 - 166x11 + 3195x10 + 419x9 + 16899x8 + 7188x7 + 67910x6 + 39372x5 + 182396x4 + 116616x3 + 322952x2 + 129952x + 274576 \( 2^{8}\cdot 5^{14}\cdot 41^{8} \) $(C_2\times Q_8).C_2^3$ (as 16T226) $[2, 2, 2]$ (GRH)
16.0.425367234731459587461873664.3 x16 + 24x12 + 532x8 - 784x4 + 9604 \( 2^{66}\cdot 7^{8} \) $(C_2\times Q_8).C_2^3$ (as 16T226) $[2]$ (GRH)
16.0.1009760059176512400000000000000.1 x16 + 105x14 + 4470x12 + 99540x10 + 1245555x8 + 8710200x6 + 31353750x4 + 45082575x2 + 3404025 \( 2^{16}\cdot 3^{12}\cdot 5^{14}\cdot 41^{6} \) $(C_2\times Q_8).C_2^3$ (as 16T226) $[2, 2, 2, 2, 1070]$ (GRH)
16.16.1009760059176512400000000000000.1 x16 - 105x14 + 4470x12 - 99540x10 + 1245555x8 - 8710200x6 + 31353750x4 - 45082575x2 + 3404025 \( 2^{16}\cdot 3^{12}\cdot 5^{14}\cdot 41^{6} \) $(C_2\times Q_8).C_2^3$ (as 16T226) $[2]$ (GRH)
16.8.1009760059176512400000000000000.1 x16 - 15x14 - 1230x12 - 1575x10 + 164205x8 + 570375x6 - 1651050x4 - 3736125x2 + 3404025 \( 2^{16}\cdot 3^{12}\cdot 5^{14}\cdot 41^{6} \) $(C_2\times Q_8).C_2^3$ (as 16T226) $[2, 2]$ (GRH)
16.8.1009760059176512400000000000000.2 x16 + 15x14 - 1230x12 + 1575x10 + 164205x8 - 570375x6 - 1651050x4 + 3736125x2 + 3404025 \( 2^{16}\cdot 3^{12}\cdot 5^{14}\cdot 41^{6} \) $(C_2\times Q_8).C_2^3$ (as 16T226) $[2, 2]$ (GRH)
16.0.258498575149187174400000000000000.1 x16 - 4x15 + 92x14 - 282x13 + 5025x12 - 11798x11 + 152482x10 - 328966x9 + 3081316x8 - 4826910x7 + 40409550x6 - 41923450x5 + 270742200x4 - 230804400x3 + 667377250x2 - 275908750x + 31721125 \( 2^{24}\cdot 3^{12}\cdot 5^{14}\cdot 41^{6} \) $(C_2\times Q_8).C_2^3$ (as 16T226) $[2, 2, 2, 2, 2140]$ (GRH)
16.16.258498575149187174400000000000000.1 x16 - 4x15 - 148x14 + 468x13 + 7455x12 - 21158x11 - 157868x10 + 460454x9 + 1427926x8 - 4645800x7 - 4381410x6 + 18195800x5 + 2364300x4 - 23793150x3 + 3291250x2 + 1823000x - 296375 \( 2^{24}\cdot 3^{12}\cdot 5^{14}\cdot 41^{6} \) $(C_2\times Q_8).C_2^3$ (as 16T226) $[4]$ (GRH)


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