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Degree Signature Ramified prime count Ramified Unramified primes
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Discriminant Root discriminant Galois root discriminant CM field Relative class number
Regulator $p$-adic completions Monogenic Index Ines. \(p\)
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Results (1-50 of at least 1000)

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Label Polynomial Discriminant Galois group Class group Regulator
4.0.392.1 $x^{4} - x^{3} + x + 1$ $2^{3}\cdot 7^{2}$ $D_{4}$ (as 4T3) trivial $0.632974319201$
4.0.784.1 $x^{4} - 3 x^{2} + 4$ $2^{4}\cdot 7^{2}$ $C_2^2$ (as 4T2) trivial $2.76865938331$
4.0.1225.1 $x^{4} - x^{3} + 5 x^{2} + 2 x + 4$ $5^{2}\cdot 7^{2}$ $C_2^2$ (as 4T2) trivial $0.962423650119$
4.2.1323.1 $x^{4} - x^{3} - 3 x^{2} - x + 1$ $-\,3^{3}\cdot 7^{2}$ $D_{4}$ (as 4T3) trivial $1.35144993247$
4.0.1421.1 $x^{4} - 2 x^{3} + 2 x^{2} - x + 2$ $7^{2}\cdot 29$ $D_{4}$ (as 4T3) trivial $2.22757871637$
4.0.1813.1 $x^{4} - 2 x^{3} + x + 2$ $7^{2}\cdot 37$ $D_{4}$ (as 4T3) trivial $2.63987071546$
4.0.2156.2 $x^{4} - x^{3} - 2 x^{2} + 2 x + 4$ $2^{2}\cdot 7^{2}\cdot 11$ $D_{4}$ (as 4T3) trivial $3.99846955784$
4.0.3136.2 $x^{4} - 2 x^{3} + 9 x^{2} - 8 x + 2$ $2^{6}\cdot 7^{2}$ $C_2^2$ (as 4T2) trivial $3.40008441411$
4.0.3528.1 $x^{4} - x^{3} + 5 x^{2} - 5 x + 4$ $2^{3}\cdot 3^{2}\cdot 7^{2}$ $D_{4}$ (as 4T3) $[2]$ $2.79876781094$
4.0.4312.1 $x^{4} - x^{3} - 3 x^{2} - x + 8$ $2^{3}\cdot 7^{2}\cdot 11$ $D_{4}$ (as 4T3) trivial $6.40056462073$
4.0.4508.2 $x^{4} - x^{3} - 6 x + 8$ $2^{2}\cdot 7^{2}\cdot 23$ $D_{4}$ (as 4T3) trivial $6.53567429615$
4.0.5341.1 $x^{4} - 2 x^{3} + 6 x^{2} - 5 x + 8$ $7^{2}\cdot 109$ $D_{4}$ (as 4T3) trivial $5.22551751307$
4.0.5929.1 $x^{4} + 9 x^{2} + 1$ $7^{2}\cdot 11^{2}$ $C_2^2$ (as 4T2) trivial $2.18464379161$
4.0.6713.1 $x^{4} - 2 x^{3} - x^{2} + 2 x + 8$ $7^{2}\cdot 137$ $D_{4}$ (as 4T3) trivial $12.6646149521$
4.0.7056.1 $x^{4} + 11 x^{2} + 25$ $2^{4}\cdot 3^{2}\cdot 7^{2}$ $C_2^2$ (as 4T2) $[2]$ $3.13359847394$
4.4.7056.1 $x^{4} - 5 x^{2} + 1$ $2^{4}\cdot 3^{2}\cdot 7^{2}$ $C_2^2$ (as 4T2) trivial $5.7128756596$
4.0.7056.2 $x^{4} - 2 x^{3} - x^{2} + 2 x + 22$ $2^{4}\cdot 3^{2}\cdot 7^{2}$ $C_2^2$ (as 4T2) $[2]$ $2.63391579385$
4.0.8281.2 $x^{4} - 3 x^{2} + 25$ $7^{2}\cdot 13^{2}$ $C_2^2$ (as 4T2) trivial $2.38952643457$
4.0.8428.2 $x^{4} - x^{3} + 4 x^{2} + 6 x + 8$ $2^{2}\cdot 7^{2}\cdot 43$ $D_{4}$ (as 4T3) trivial $9.73447587067$
4.0.9016.2 $x^{4} - x^{3} - 2 x^{2} + 9 x + 11$ $2^{3}\cdot 7^{2}\cdot 23$ $D_{4}$ (as 4T3) trivial $4.02734075184$
4.2.9408.2 $x^{4} - 2 x^{3} - 6 x + 9$ $-\,2^{6}\cdot 3\cdot 7^{2}$ $D_{4}$ (as 4T3) trivial $9.40204384113$
4.0.11025.1 $x^{4} - x^{3} + 4 x^{2} - 15 x + 15$ $3^{2}\cdot 5^{2}\cdot 7^{2}$ $C_2^2$ (as 4T2) $[2]$ $3.13359847394$
4.4.11025.1 $x^{4} - 13 x^{2} + 16$ $3^{2}\cdot 5^{2}\cdot 7^{2}$ $C_2^2$ (as 4T2) trivial $6.64477622728$
4.0.11025.2 $x^{4} + 11 x^{2} + 4$ $3^{2}\cdot 5^{2}\cdot 7^{2}$ $C_2^2$ (as 4T2) $[2]$ $8.81314098615$
4.0.11417.2 $x^{4} - 2 x^{3} + 7 x^{2} - 6 x + 16$ $7^{2}\cdot 233$ $D_{4}$ (as 4T3) trivial $18.0164890918$
4.0.12397.2 $x^{4} - 2 x^{3} + 2 x^{2} - x + 16$ $7^{2}\cdot 11\cdot 23$ $D_{4}$ (as 4T3) trivial $8.63060244424$
4.0.12544.1 $x^{4} + 8 x^{2} + 9$ $2^{8}\cdot 7^{2}$ $C_2^2$ (as 4T2) $[4]$ $2.76865938331$
4.0.12544.2 $x^{4} + 49$ $2^{8}\cdot 7^{2}$ $C_2^2$ (as 4T2) $[4]$ $3.40008441411$
4.0.12789.1 $x^{4} - 2 x^{3} + x + 16$ $3^{2}\cdot 7^{2}\cdot 29$ $D_{4}$ (as 4T3) $[2]$ $4.16348864333$
4.0.13132.2 $x^{4} - x^{3} + 5 x^{2} - 12 x + 18$ $2^{2}\cdot 7^{2}\cdot 67$ $D_{4}$ (as 4T3) trivial $5.20419011527$
4.0.13769.1 $x^{4} - 2 x^{3} - 5 x^{2} + 6 x + 16$ $7^{2}\cdot 281$ $D_{4}$ (as 4T3) trivial $20.2451842028$
4.0.13916.2 $x^{4} - x^{3} - 3 x^{2} - 8 x + 22$ $2^{2}\cdot 7^{2}\cdot 71$ $D_{4}$ (as 4T3) trivial $4.7619559584$
4.0.14161.1 $x^{4} - 5 x^{2} + 36$ $7^{2}\cdot 17^{2}$ $C_2^2$ (as 4T2) $[5]$ $4.18942509452$
4.0.15484.1 $x^{4} - x^{3} - 7 x^{2} + 8 x + 22$ $2^{2}\cdot 7^{2}\cdot 79$ $D_{4}$ (as 4T3) trivial $5.27691511571$
4.0.16317.2 $x^{4} - 2 x^{3} + 6 x^{2} - 5 x + 22$ $3^{2}\cdot 7^{2}\cdot 37$ $D_{4}$ (as 4T3) $[2]$ $4.96971749814$
4.0.16513.1 $x^{4} - 2 x^{3} + 9 x^{2} - 8 x + 23$ $7^{2}\cdot 337$ $D_{4}$ (as 4T3) trivial $3.59264479079$
4.0.16856.1 $x^{4} - x^{3} + 7 x^{2} - 13 x + 22$ $2^{3}\cdot 7^{2}\cdot 43$ $D_{4}$ (as 4T3) trivial $14.1943811486$
4.0.17248.3 $x^{4} - 5 x^{2} + 22$ $2^{5}\cdot 7^{2}\cdot 11$ $D_{4}$ (as 4T3) $[2]$ $4.29741767551$
4.2.17444.1 $x^{4} - x^{3} - 2 x^{2} - 5 x - 3$ $-\,2^{2}\cdot 7^{2}\cdot 89$ $S_4$ (as 4T5) trivial $11.0177158457$
4.0.19061.1 $x^{4} - 2 x^{3} - 8 x^{2} + 9 x + 22$ $7^{2}\cdot 389$ $D_{4}$ (as 4T3) trivial $10.3854398565$
4.0.19404.1 $x^{4} - x^{3} + 11 x^{2} - 8 x + 22$ $2^{2}\cdot 3^{2}\cdot 7^{2}\cdot 11$ $D_{4}$ (as 4T3) $[2]$ $2.88446488466$
4.4.19600.1 $x^{4} - 2 x^{3} - 15 x^{2} + 16 x + 29$ $2^{4}\cdot 5^{2}\cdot 7^{2}$ $C_2^2$ (as 4T2) trivial $6.60263997027$
4.0.19600.2 $x^{4} - 17 x^{2} + 81$ $2^{4}\cdot 5^{2}\cdot 7^{2}$ $C_2^2$ (as 4T2) $[2]$ $4.95577746058$
4.0.19649.1 $x^{4} - 2 x^{3} - 7 x^{2} + 8 x + 23$ $7^{2}\cdot 401$ $D_{4}$ (as 4T3) trivial $3.73769760687$
4.2.20727.2 $x^{4} - x^{3} - 2 x^{2} + 9 x - 3$ $-\,3^{2}\cdot 7^{2}\cdot 47$ $D_{4}$ (as 4T3) trivial $11.7068873209$
4.2.20727.3 $x^{4} - 2 x^{3} - 7 x^{2} + 8 x - 5$ $-\,3^{2}\cdot 7^{2}\cdot 47$ $D_{4}$ (as 4T3) trivial $7.33569336447$
4.0.20776.1 $x^{4} - x^{3} + 11 x^{2} - x + 22$ $2^{3}\cdot 7^{2}\cdot 53$ $D_{4}$ (as 4T3) $[2]$ $8.19589383834$
4.0.20776.2 $x^{4} - x^{3} + 4 x^{2} - 15 x + 29$ $2^{3}\cdot 7^{2}\cdot 53$ $D_{4}$ (as 4T3) $[2]$ $3.05628951175$
4.0.20972.1 $x^{4} - x^{3} + 7 x^{2} + 8 x + 22$ $2^{2}\cdot 7^{2}\cdot 107$ $D_{4}$ (as 4T3) trivial $5.22084933116$
4.0.23177.2 $x^{4} - 2 x^{3} - x^{2} + 2 x + 29$ $7^{2}\cdot 11\cdot 43$ $D_{4}$ (as 4T3) trivial $3.10590857455$
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