↑

Learn more

Refine search

Degree Signature Class number Class group structure CM field
Ramified prime count Ramified Unramified primes Galois group Galois
Discriminant Root discriminant Galois root discriminant Regulator Intermediate field
$p$-adic completions Minimal sibling Monogenic Index Ines. \(p\)
Sort order Select

Results (1-50 of 234526 matches)

Next   displayed columns for results
Label Polynomial Discriminant Galois group Class group Regulator
4.0.4232.1 $x^{4} - x^{3} + 4 x^{2} + x + 1$ $2^{3}\cdot 23^{2}$ $D_{4}$ (as 4T3) $[3]$ $1.42903624604$
4.0.4761.1 $x^{4} - x^{3} - 5 x^{2} - 6 x + 36$ $3^{2}\cdot 23^{2}$ $C_2^2$ (as 4T2) $[3]$ $3.21727197116$
4.0.6348.1 $x^{4} - x^{3} + 2 x^{2} + 2 x + 4$ $2^{2}\cdot 3\cdot 23^{2}$ $D_{4}$ (as 4T3) $[3]$ $3.25105926917$
4.0.8464.1 $x^{4} - 11 x^{2} + 36$ $2^{4}\cdot 23^{2}$ $C_2^2$ (as 4T2) $[3]$ $3.87076670029$
4.0.12696.1 $x^{4} + x^{2} + 6$ $2^{3}\cdot 3\cdot 23^{2}$ $D_{4}$ (as 4T3) $[3]$ $5.05227152969$
4.0.13225.1 $x^{4} + 9 x^{2} + 49$ $5^{2}\cdot 23^{2}$ $C_2^2$ (as 4T2) $[3]$ $0.962423650119$
4.0.15341.1 $x^{4} - x^{3} - 2 x^{2} + 4 x + 16$ $23^{2}\cdot 29$ $D_{4}$ (as 4T3) $[3]$ $4.95582776355$
4.0.33856.1 $x^{4} - 2 x^{3} + 17 x^{2} - 16 x + 18$ $2^{6}\cdot 23^{2}$ $C_2^2$ (as 4T2) $[3]$ $10.7928181024$
4.0.38617.1 $x^{4} - x^{3} + 11 x^{2} - 14 x + 12$ $23^{2}\cdot 73$ $D_{4}$ (as 4T3) $[3]$ $5.85978636459$
4.2.43907.1 $x^{4} - x^{3} - 6 x^{2} + 6 x + 13$ $-\,23^{2}\cdot 83$ $S_4$ (as 4T5) trivial $8.16125154084$
4.0.49197.1 $x^{4} - 2 x^{3} + 2 x^{2} - x + 6$ $3\cdot 23^{2}\cdot 31$ $D_{4}$ (as 4T3) $[3]$ $12.5133826084$
4.0.50784.2 $x^{4} + 2 x^{2} + 24$ $2^{5}\cdot 3\cdot 23^{2}$ $D_{4}$ (as 4T3) $[6]$ $5.4534870683$
4.2.52371.2 $x^{4} - 2 x^{3} + 2 x^{2} - x - 17$ $-\,3^{2}\cdot 11\cdot 23^{2}$ $D_{4}$ (as 4T3) trivial $6.89883374468$
4.0.55016.1 $x^{4} + 9 x^{2} + 26$ $2^{3}\cdot 13\cdot 23^{2}$ $D_{4}$ (as 4T3) $[6]$ $3.09796833248$
4.0.55016.2 $x^{4} - x^{3} - 5 x^{2} + 17 x + 36$ $2^{3}\cdot 13\cdot 23^{2}$ $D_{4}$ (as 4T3) $[6]$ $7.57917370863$
4.2.59248.2 $x^{4} - 2 x^{3} - x^{2} + 2 x - 22$ $-\,2^{4}\cdot 7\cdot 23^{2}$ $D_{4}$ (as 4T3) trivial $25.2980704295$
4.4.61893.1 $x^{4} - 11 x^{2} + 13$ $3^{2}\cdot 13\cdot 23^{2}$ $D_{4}$ (as 4T3) trivial $23.1117061375$
4.0.61893.2 $x^{4} - x^{3} + 4 x^{2} + 24 x + 24$ $3^{2}\cdot 13\cdot 23^{2}$ $D_{4}$ (as 4T3) $[6]$ $5.56373853662$
4.0.61893.3 $x^{4} - x^{3} + 41 x^{2} - 29 x + 427$ $3^{2}\cdot 13\cdot 23^{2}$ $D_{4}$ (as 4T3) $[2]$ $6.36258861522$
4.0.65596.1 $x^{4} - x^{3} - x^{2} - 8 x + 18$ $2^{2}\cdot 23^{2}\cdot 31$ $D_{4}$ (as 4T3) $[3]$ $11.4627712628$
4.2.71415.2 $x^{4} - x^{3} - 6 x^{2} + 29 x + 13$ $-\,3^{3}\cdot 5\cdot 23^{2}$ $D_{4}$ (as 4T3) trivial $22.4165166239$
4.0.74589.1 $x^{4} - 2 x^{3} - 2 x^{2} + 3 x + 8$ $3\cdot 23^{2}\cdot 47$ $D_{4}$ (as 4T3) $[3]$ $9.37404585242$
4.0.76176.1 $x^{4} + 35 x^{2} + 289$ $2^{4}\cdot 3^{2}\cdot 23^{2}$ $C_2^2$ (as 4T2) $[4]$ $6.43454394231$
4.0.76176.3 $x^{4} + 23 x^{2} + 529$ $2^{4}\cdot 3^{2}\cdot 23^{2}$ $C_2^2$ (as 4T2) $[4]$ $7.74153340057$
4.0.82524.2 $x^{4} + 8 x^{2} + 39$ $2^{2}\cdot 3\cdot 13\cdot 23^{2}$ $D_{4}$ (as 4T3) $[6]$ $11.9815156858$
4.0.82524.3 $x^{4} - x^{3} - 6 x^{2} - 17 x + 59$ $2^{2}\cdot 3\cdot 13\cdot 23^{2}$ $D_{4}$ (as 4T3) $[6]$ $4.73791824176$
4.0.91517.1 $x^{4} - 2 x^{3} + 6 x^{2} - 5 x + 12$ $23^{2}\cdot 173$ $D_{4}$ (as 4T3) $[3]$ $14.8055844754$
4.0.93633.1 $x^{4} - x^{3} - 10 x^{2} + 8 x + 64$ $3\cdot 23^{2}\cdot 59$ $D_{4}$ (as 4T3) $[3]$ $27.0508637982$
4.0.99452.1 $x^{4} - x^{3} + 10 x^{2} - 2 x + 4$ $2^{2}\cdot 23^{2}\cdot 47$ $D_{4}$ (as 4T3) $[3]$ $21.5406111228$
4.0.101568.2 $x^{4} - 10 x^{2} + 48$ $2^{6}\cdot 3\cdot 23^{2}$ $D_{4}$ (as 4T3) $[6]$ $8.29137664073$
4.0.102097.1 $x^{4} - x^{3} + 12 x^{2} + 20 x + 32$ $23^{2}\cdot 193$ $D_{4}$ (as 4T3) $[3]$ $22.418741716$
4.0.104213.1 $x^{4} - x^{3} - 8 x^{2} - 16 x + 72$ $23^{2}\cdot 197$ $D_{4}$ (as 4T3) $[3]$ $15.2425571526$
4.0.110032.1 $x^{4} + x^{2} + 52$ $2^{4}\cdot 13\cdot 23^{2}$ $D_{4}$ (as 4T3) $[6]$ $11.2221232715$
4.0.112677.1 $x^{4} - 2 x^{3} - 4 x^{2} + 5 x + 12$ $3\cdot 23^{2}\cdot 71$ $D_{4}$ (as 4T3) $[3]$ $20.2227930428$
4.4.119025.1 $x^{4} - 37 x^{2} + 256$ $3^{2}\cdot 5^{2}\cdot 23^{2}$ $C_2^2$ (as 4T2) trivial $29.4529804132$
4.0.119025.3 $x^{4} - x^{3} - 28 x^{2} - 29 x + 841$ $3^{2}\cdot 5^{2}\cdot 23^{2}$ $C_2^2$ (as 4T2) $[2]$ $19.0241465244$
4.0.124844.2 $x^{4} + 12 x^{2} + 59$ $2^{2}\cdot 23^{2}\cdot 59$ $D_{4}$ (as 4T3) $[3]$ $9.19179466159$
4.0.131192.1 $x^{4} - 15 x^{2} + 62$ $2^{3}\cdot 23^{2}\cdot 31$ $D_{4}$ (as 4T3) $[3]$ $26.0861242778$
4.0.135424.1 $x^{4} + 24 x^{2} + 121$ $2^{8}\cdot 23^{2}$ $C_2^2$ (as 4T2) $[4]$ $3.87076670029$
4.0.135424.2 $x^{4} + 529$ $2^{8}\cdot 23^{2}$ $C_2^2$ (as 4T2) $[4]$ $10.7928181024$
4.0.142301.1 $x^{4} - x^{3} + 13 x^{2} - 38 x + 64$ $23^{2}\cdot 269$ $D_{4}$ (as 4T3) $[3]$ $19.1538962725$
4.2.145475.1 $x^{4} - x^{3} - 6 x^{2} - 40 x - 355$ $-\,5^{2}\cdot 11\cdot 23^{2}$ $D_{4}$ (as 4T3) trivial $15.814012139$
4.0.146533.1 $x^{4} - x^{3} - 13 x^{2} - 2 x + 96$ $23^{2}\cdot 277$ $D_{4}$ (as 4T3) $[3]$ $29.8024864839$
4.0.150236.1 $x^{4} - x^{3} + 4 x^{2} - 22 x + 24$ $2^{2}\cdot 23^{2}\cdot 71$ $D_{4}$ (as 4T3) $[3]$ $27.2022213708$
4.0.152352.1 $x^{4} + 9 x^{2} + 72$ $2^{5}\cdot 3^{2}\cdot 23^{2}$ $D_{4}$ (as 4T3) $[2, 6]$ $3.49469393936$
4.0.152881.1 $x^{4} + 3 x^{2} + 100$ $17^{2}\cdot 23^{2}$ $C_2^2$ (as 4T2) $[21]$ $4.18942509452$
4.0.158700.2 $x^{4} - x^{3} - 13 x^{2} + 21 x + 96$ $2^{2}\cdot 3\cdot 5^{2}\cdot 23^{2}$ $D_{4}$ (as 4T3) $[6]$ $10.8609594616$
4.2.160816.2 $x^{4} - 2 x^{3} - 8 x^{2} - 14 x + 3$ $-\,2^{4}\cdot 19\cdot 23^{2}$ $S_4$ (as 4T5) trivial $48.0457534938$
4.0.165048.2 $x^{4} - x^{3} + 12 x^{2} - 3 x + 9$ $2^{3}\cdot 3\cdot 13\cdot 23^{2}$ $D_{4}$ (as 4T3) $[6]$ $7.14904203976$
4.0.165048.4 $x^{4} - x^{3} + 15 x^{2} - 39 x + 72$ $2^{3}\cdot 3\cdot 13\cdot 23^{2}$ $D_{4}$ (as 4T3) $[6]$ $17.8601231981$
Next   displayed columns for results