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Degree Signature Discriminant Root discriminant Galois root discriminant
Ramified prime count Ramified Unramified primes Maximum ramified prime Galois group
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Results (1-50 of 31117 matches)

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Label Polynomial Discriminant Galois group Class group Regulator
4.0.6144.2 $x^{4} + 4 x^{2} + 6$ $2^{11}\cdot 3$ $D_{4}$ (as 4T3) trivial $3.6261872399$
4.0.22528.2 $x^{4} + 4 x^{2} + 22$ $2^{11}\cdot 11$ $D_{4}$ (as 4T3) trivial $15.9474576289$
4.2.26624.2 $x^{4} - 8 x^{2} - 8 x + 2$ $-\,2^{11}\cdot 13$ $S_4$ (as 4T5) trivial $12.7781788739$
4.0.38912.1 $x^{4} - 12 x^{2} + 38$ $2^{11}\cdot 19$ $D_{4}$ (as 4T3) trivial $14.2979404109$
4.0.88064.1 $x^{4} - 12 x^{2} + 86$ $2^{11}\cdot 43$ $D_{4}$ (as 4T3) trivial $16.5137573297$
4.0.104448.2 $x^{4} + 20 x^{2} + 102$ $2^{11}\cdot 3\cdot 17$ $D_{4}$ (as 4T3) $[2]$ $14.7058688502$
4.0.104448.4 $x^{4} + 4 x^{2} + 102$ $2^{11}\cdot 3\cdot 17$ $D_{4}$ (as 4T3) $[2]$ $5.77947415702$
4.0.120832.2 $x^{4} + 20 x^{2} + 118$ $2^{11}\cdot 59$ $D_{4}$ (as 4T3) trivial $9.08998063132$
4.0.137216.1 $x^{4} - 12 x^{2} + 134$ $2^{11}\cdot 67$ $D_{4}$ (as 4T3) trivial $25.3479316858$
4.0.153600.4 $x^{4} + 20 x^{2} + 150$ $2^{11}\cdot 3\cdot 5^{2}$ $D_{4}$ (as 4T3) $[2]$ $17.8670144702$
4.0.169984.2 $x^{4} + 4 x^{2} + 166$ $2^{11}\cdot 83$ $D_{4}$ (as 4T3) trivial $53.6619426256$
4.2.190464.2 $x^{4} - 8 x^{2} - 24 x - 14$ $-\,2^{11}\cdot 3\cdot 31$ $S_4$ (as 4T5) trivial $42.4193337561$
4.0.202752.5 $x^{4} - 12 x^{2} + 198$ $2^{11}\cdot 3^{2}\cdot 11$ $D_{4}$ (as 4T3) $[2, 2]$ $7.20742950354$
4.0.219136.1 $x^{4} - 28 x^{2} + 214$ $2^{11}\cdot 107$ $D_{4}$ (as 4T3) trivial $17.3146630206$
4.0.251904.1 $x^{4} - 28 x^{2} + 246$ $2^{11}\cdot 3\cdot 41$ $D_{4}$ (as 4T3) $[2]$ $20.8475394696$
4.0.251904.4 $x^{4} + 4 x^{2} + 246$ $2^{11}\cdot 3\cdot 41$ $D_{4}$ (as 4T3) $[2]$ $12.3817192337$
4.0.268288.2 $x^{4} + 20 x^{2} + 262$ $2^{11}\cdot 131$ $D_{4}$ (as 4T3) trivial $12.0444344591$
4.0.284672.1 $x^{4} - 12 x^{2} + 278$ $2^{11}\cdot 139$ $D_{4}$ (as 4T3) $[3]$ $9.90378746507$
4.0.301056.1 $x^{4} - 28 x^{2} + 294$ $2^{11}\cdot 3\cdot 7^{2}$ $D_{4}$ (as 4T3) $[6]$ $7.81138314421$
4.0.333824.2 $x^{4} - 8 x^{2} - 8 x + 34$ $2^{11}\cdot 163$ $S_4$ (as 4T5) $[2]$ $10.5358034206$
4.0.333824.4 $x^{4} + 36 x^{2} + 326$ $2^{11}\cdot 163$ $D_{4}$ (as 4T3) $[5]$ $7.86249468038$
4.0.350208.2 $x^{4} + 36 x^{2} + 342$ $2^{11}\cdot 3^{2}\cdot 19$ $D_{4}$ (as 4T3) $[2, 2]$ $5.6833842858$
4.0.366592.1 $x^{4} - 28 x^{2} + 358$ $2^{11}\cdot 179$ $D_{4}$ (as 4T3) $[3]$ $7.90996810151$
4.0.382976.2 $x^{4} + 36 x^{2} + 374$ $2^{11}\cdot 11\cdot 17$ $D_{4}$ (as 4T3) $[2]$ $20.4979305291$
4.0.382976.3 $x^{4} - 12 x^{2} + 374$ $2^{11}\cdot 11\cdot 17$ $D_{4}$ (as 4T3) $[2]$ $21.2117703267$
4.2.387072.1 $x^{4} - 12 x^{2} - 16 x - 42$ $-\,2^{11}\cdot 3^{3}\cdot 7$ $S_4$ (as 4T5) trivial $78.7202158842$
4.0.432128.2 $x^{4} + 36 x^{2} + 422$ $2^{11}\cdot 211$ $D_{4}$ (as 4T3) trivial $52.3277956778$
4.0.448512.1 $x^{4} - 28 x^{2} + 438$ $2^{11}\cdot 3\cdot 73$ $D_{4}$ (as 4T3) $[2]$ $32.8800977971$
4.0.448512.4 $x^{4} + 20 x^{2} + 438$ $2^{11}\cdot 3\cdot 73$ $D_{4}$ (as 4T3) $[2]$ $29.261740667$
4.0.464896.2 $x^{4} + 4 x^{2} + 454$ $2^{11}\cdot 227$ $D_{4}$ (as 4T3) trivial $74.3163750962$
4.4.497664.1 $x^{4} - 24 x^{2} - 56 x - 30$ $2^{11}\cdot 3^{5}$ $S_4$ (as 4T5) trivial $110.200394557$
4.2.501760.2 $x^{4} + 4 x^{2} - 10$ $-\,2^{11}\cdot 5\cdot 7^{2}$ $D_{4}$ (as 4T3) trivial $66.693118953$
4.2.501760.5 $x^{4} - 8 x^{2} - 40$ $-\,2^{11}\cdot 5\cdot 7^{2}$ $D_{4}$ (as 4T3) trivial $49.5815472699$
4.0.514048.1 $x^{4} - 44 x^{2} + 502$ $2^{11}\cdot 251$ $D_{4}$ (as 4T3) $[9]$ $10.4770356147$
4.0.546816.1 $x^{4} - 44 x^{2} + 534$ $2^{11}\cdot 3\cdot 89$ $D_{4}$ (as 4T3) $[2]$ $18.1098336911$
4.0.546816.3 $x^{4} - 28 x^{2} + 534$ $2^{11}\cdot 3\cdot 89$ $D_{4}$ (as 4T3) $[4]$ $16.5138865203$
4.0.563200.2 $x^{4} + 20 x^{2} + 550$ $2^{11}\cdot 5^{2}\cdot 11$ $D_{4}$ (as 4T3) $[2]$ $11.0692045011$
4.0.579584.2 $x^{4} + 36 x^{2} + 566$ $2^{11}\cdot 283$ $D_{4}$ (as 4T3) trivial $60.6277215839$
4.0.595968.1 $x^{4} - 44 x^{2} + 582$ $2^{11}\cdot 3\cdot 97$ $D_{4}$ (as 4T3) $[2]$ $12.8423596541$
4.0.595968.4 $x^{4} + 4 x^{2} + 582$ $2^{11}\cdot 3\cdot 97$ $D_{4}$ (as 4T3) $[2]$ $18.8901092312$
4.0.628736.1 $x^{4} - 12 x^{2} + 614$ $2^{11}\cdot 307$ $D_{4}$ (as 4T3) trivial $33.8938948063$
4.0.661504.1 $x^{4} - 44 x^{2} + 646$ $2^{11}\cdot 17\cdot 19$ $D_{4}$ (as 4T3) $[2]$ $52.7937614367$
4.0.661504.3 $x^{4} - 28 x^{2} + 646$ $2^{11}\cdot 17\cdot 19$ $D_{4}$ (as 4T3) $[2]$ $12.5955344022$
4.0.677888.2 $x^{4} + 36 x^{2} + 662$ $2^{11}\cdot 331$ $D_{4}$ (as 4T3) trivial $41.9258477915$
4.0.694272.2 $x^{4} + 52 x^{2} + 678$ $2^{11}\cdot 3\cdot 113$ $D_{4}$ (as 4T3) $[2]$ $19.2052511684$
4.0.694272.4 $x^{4} + 20 x^{2} + 678$ $2^{11}\cdot 3\cdot 113$ $D_{4}$ (as 4T3) $[8]$ $8.22918224324$
4.0.710656.2 $x^{4} + 52 x^{2} + 694$ $2^{11}\cdot 347$ $D_{4}$ (as 4T3) trivial $121.663975762$
4.0.743424.1 $x^{4} - 44 x^{2} + 726$ $2^{11}\cdot 3\cdot 11^{2}$ $D_{4}$ (as 4T3) $[2, 2]$ $8.26307370595$
4.2.747520.2 $x^{4} - 24 x^{2} - 56 x - 46$ $-\,2^{11}\cdot 5\cdot 73$ $S_4$ (as 4T5) trivial $56.3158605731$
4.0.776192.1 $x^{4} - 12 x^{2} + 758$ $2^{11}\cdot 379$ $D_{4}$ (as 4T3) trivial $63.1300211031$
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