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Degree Signature Discriminant Root discriminant Galois root discriminant
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Label Polynomial Discriminant Galois group Class group Regulator
4.0.6144.1 $x^{4} - 4 x^{2} + 6$ $2^{11}\cdot 3$ $D_{4}$ (as 4T3) trivial $5.87031458579$
4.0.22528.1 $x^{4} - 4 x^{2} + 22$ $2^{11}\cdot 11$ $D_{4}$ (as 4T3) trivial $5.42303437104$
4.0.38912.2 $x^{4} + 12 x^{2} + 38$ $2^{11}\cdot 19$ $D_{4}$ (as 4T3) trivial $12.3060519726$
4.0.88064.2 $x^{4} + 12 x^{2} + 86$ $2^{11}\cdot 43$ $D_{4}$ (as 4T3) trivial $21.2806136581$
4.0.104448.1 $x^{4} - 20 x^{2} + 102$ $2^{11}\cdot 3\cdot 17$ $D_{4}$ (as 4T3) $[2]$ $6.18288222112$
4.0.104448.3 $x^{4} - 4 x^{2} + 102$ $2^{11}\cdot 3\cdot 17$ $D_{4}$ (as 4T3) $[2]$ $16.2114259933$
4.2.108544.1 $x^{4} - 8 x + 2$ $-\,2^{11}\cdot 53$ $S_4$ (as 4T5) trivial $15.2526461983$
4.0.120832.1 $x^{4} - 20 x^{2} + 118$ $2^{11}\cdot 59$ $D_{4}$ (as 4T3) trivial $41.7535349831$
4.0.137216.2 $x^{4} + 12 x^{2} + 134$ $2^{11}\cdot 67$ $D_{4}$ (as 4T3) trivial $27.9877973952$
4.0.153600.3 $x^{4} - 20 x^{2} + 150$ $2^{11}\cdot 3\cdot 5^{2}$ $D_{4}$ (as 4T3) $[2]$ $8.16781508389$
4.0.169984.1 $x^{4} - 4 x^{2} + 166$ $2^{11}\cdot 83$ $D_{4}$ (as 4T3) trivial $9.37153608582$
4.2.174080.1 $x^{4} - 8 x^{2} - 32 x - 40$ $-\,2^{11}\cdot 5\cdot 17$ $S_4$ (as 4T5) trivial $41.0114177134$
4.0.202752.6 $x^{4} + 12 x^{2} + 198$ $2^{11}\cdot 3^{2}\cdot 11$ $D_{4}$ (as 4T3) $[2, 2]$ $6.11177270275$
4.2.206848.1 $x^{4} - 8 x - 46$ $-\,2^{11}\cdot 101$ $S_4$ (as 4T5) trivial $21.5900259398$
4.0.219136.2 $x^{4} + 28 x^{2} + 214$ $2^{11}\cdot 107$ $D_{4}$ (as 4T3) trivial $55.0019495557$
4.0.251904.2 $x^{4} + 28 x^{2} + 246$ $2^{11}\cdot 3\cdot 41$ $D_{4}$ (as 4T3) $[2]$ $15.044328665$
4.0.251904.3 $x^{4} - 4 x^{2} + 246$ $2^{11}\cdot 3\cdot 41$ $D_{4}$ (as 4T3) $[2]$ $18.5229929931$
4.0.268288.1 $x^{4} - 20 x^{2} + 262$ $2^{11}\cdot 131$ $D_{4}$ (as 4T3) trivial $70.5191252962$
4.0.284672.2 $x^{4} + 12 x^{2} + 278$ $2^{11}\cdot 139$ $D_{4}$ (as 4T3) trivial $40.2734489342$
4.0.301056.2 $x^{4} + 28 x^{2} + 294$ $2^{11}\cdot 3\cdot 7^{2}$ $D_{4}$ (as 4T3) $[2]$ $13.6525655437$
4.4.333824.1 $x^{4} - 20 x^{2} - 32 x + 6$ $2^{11}\cdot 163$ $S_4$ (as 4T5) trivial $97.5863796943$
4.0.333824.3 $x^{4} - 36 x^{2} + 326$ $2^{11}\cdot 163$ $D_{4}$ (as 4T3) trivial $38.2305568518$
4.0.350208.1 $x^{4} - 36 x^{2} + 342$ $2^{11}\cdot 3^{2}\cdot 19$ $D_{4}$ (as 4T3) $[2, 2]$ $9.73310948528$
4.0.366592.2 $x^{4} + 28 x^{2} + 358$ $2^{11}\cdot 179$ $D_{4}$ (as 4T3) trivial $77.0300387098$
4.0.382976.1 $x^{4} - 36 x^{2} + 374$ $2^{11}\cdot 11\cdot 17$ $D_{4}$ (as 4T3) $[2]$ $23.7981291306$
4.0.382976.4 $x^{4} + 12 x^{2} + 374$ $2^{11}\cdot 11\cdot 17$ $D_{4}$ (as 4T3) $[2]$ $18.1209459954$
4.0.432128.1 $x^{4} - 36 x^{2} + 422$ $2^{11}\cdot 211$ $D_{4}$ (as 4T3) trivial $32.7300012317$
4.2.436224.1 $x^{4} - 16 x^{2} - 8 x + 50$ $-\,2^{11}\cdot 3\cdot 71$ $S_4$ (as 4T5) trivial $54.6053656355$
4.0.448512.2 $x^{4} + 28 x^{2} + 438$ $2^{11}\cdot 3\cdot 73$ $D_{4}$ (as 4T3) $[2]$ $8.21167385335$
4.0.448512.3 $x^{4} - 20 x^{2} + 438$ $2^{11}\cdot 3\cdot 73$ $D_{4}$ (as 4T3) $[2]$ $17.1385937811$
4.0.464896.1 $x^{4} - 4 x^{2} + 454$ $2^{11}\cdot 227$ $D_{4}$ (as 4T3) trivial $29.0115704757$
4.0.497664.1 $x^{4} + 12 x^{2} - 16 x + 6$ $2^{11}\cdot 3^{5}$ $S_4$ (as 4T5) $[2]$ $32.9367204391$
4.2.501760.1 $x^{4} - 4 x^{2} - 10$ $-\,2^{11}\cdot 5\cdot 7^{2}$ $D_{4}$ (as 4T3) trivial $66.870226506$
4.2.501760.4 $x^{4} - 56 x + 98$ $-\,2^{11}\cdot 5\cdot 7^{2}$ $S_4$ (as 4T5) trivial $51.512805081$
4.2.501760.6 $x^{4} + 8 x^{2} - 40$ $-\,2^{11}\cdot 5\cdot 7^{2}$ $D_{4}$ (as 4T3) trivial $22.8822316619$
4.0.514048.2 $x^{4} + 44 x^{2} + 502$ $2^{11}\cdot 251$ $D_{4}$ (as 4T3) trivial $23.4766819315$
4.0.546816.2 $x^{4} + 44 x^{2} + 534$ $2^{11}\cdot 3\cdot 89$ $D_{4}$ (as 4T3) $[2]$ $33.8805399775$
4.0.546816.4 $x^{4} + 28 x^{2} + 534$ $2^{11}\cdot 3\cdot 89$ $D_{4}$ (as 4T3) $[4]$ $8.31079428172$
4.0.563200.1 $x^{4} - 20 x^{2} + 550$ $2^{11}\cdot 5^{2}\cdot 11$ $D_{4}$ (as 4T3) $[2]$ $50.9117642828$
4.0.579584.1 $x^{4} - 36 x^{2} + 566$ $2^{11}\cdot 283$ $D_{4}$ (as 4T3) trivial $44.8884232405$
4.0.595968.2 $x^{4} + 44 x^{2} + 582$ $2^{11}\cdot 3\cdot 97$ $D_{4}$ (as 4T3) $[2]$ $30.7630000432$
4.0.595968.3 $x^{4} - 4 x^{2} + 582$ $2^{11}\cdot 3\cdot 97$ $D_{4}$ (as 4T3) $[2]$ $37.0395365374$
4.2.600064.2 $x^{4} - 20 x^{2} - 16 x + 76$ $-\,2^{11}\cdot 293$ $S_4$ (as 4T5) trivial $44.6433538888$
4.2.616448.2 $x^{4} - 20 x^{2} - 16 x + 140$ $-\,2^{11}\cdot 7\cdot 43$ $S_4$ (as 4T5) trivial $93.7222924061$
4.0.628736.2 $x^{4} + 12 x^{2} + 614$ $2^{11}\cdot 307$ $D_{4}$ (as 4T3) trivial $60.2404468683$
4.0.661504.2 $x^{4} + 44 x^{2} + 646$ $2^{11}\cdot 17\cdot 19$ $D_{4}$ (as 4T3) $[2]$ $13.6886263186$
4.0.661504.4 $x^{4} + 28 x^{2} + 646$ $2^{11}\cdot 17\cdot 19$ $D_{4}$ (as 4T3) $[10]$ $9.99688412702$
4.0.677888.1 $x^{4} - 36 x^{2} + 662$ $2^{11}\cdot 331$ $D_{4}$ (as 4T3) trivial $54.2003011152$
4.0.694272.1 $x^{4} - 52 x^{2} + 678$ $2^{11}\cdot 3\cdot 113$ $D_{4}$ (as 4T3) $[2]$ $39.1058777818$
4.0.694272.3 $x^{4} - 20 x^{2} + 678$ $2^{11}\cdot 3\cdot 113$ $D_{4}$ (as 4T3) $[4]$ $7.41891840206$
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