Refine search

Degree Signature Discriminant Root discriminant Galois root discriminant
Ramified prime count Ramified Unramified primes Maximum ramified prime Galois group
Class group structure Class number Regulator Intermediate field Field is
Narrow class group Narrow class number Relative class number CM field $p$-adic completions
Monogenic Index Ines. \(p\) Minimal sibling Unit signature rank
Sort order Select

Results (1-50 of at least 1000)

Next   To download results, determine the number of results.
Label Polynomial Discriminant Galois group Class group Regulator
4.4.2048.1 $x^{4} - 4 x^{2} + 2$ $2^{11}$ $C_4$ (as 4T1) trivial $2.44179500662$
4.0.34816.1 $x^{4} + 12 x^{2} + 34$ $2^{11}\cdot 17$ $D_{4}$ (as 4T3) $[4]$ $1.76274717404$
4.2.63488.2 $x^{4} + 12 x^{2} - 62$ $-\,2^{11}\cdot 31$ $D_{4}$ (as 4T3) $[2]$ $8.91501046485$
4.2.96256.1 $x^{4} - 4 x^{2} - 94$ $-\,2^{11}\cdot 47$ $D_{4}$ (as 4T3) $[2]$ $9.28736775114$
4.0.100352.5 $x^{4} + 28 x^{2} + 98$ $2^{11}\cdot 7^{2}$ $C_4$ (as 4T1) $[2, 2]$ $1.76274717404$
4.2.129024.2 $x^{4} + 12 x^{2} - 126$ $-\,2^{11}\cdot 3^{2}\cdot 7$ $D_{4}$ (as 4T3) $[2]$ $11.4021192511$
4.2.161792.1 $x^{4} - 4 x^{2} - 158$ $-\,2^{11}\cdot 79$ $D_{4}$ (as 4T3) $[4]$ $5.92084142701$
4.0.198656.1 $x^{4} + 28 x^{2} + 194$ $2^{11}\cdot 97$ $D_{4}$ (as 4T3) $[8]$ $1.76274717404$
4.4.231424.1 $x^{4} - 36 x^{2} + 226$ $2^{11}\cdot 113$ $D_{4}$ (as 4T3) $[2]$ $25.5413440749$
4.2.260096.2 $x^{4} + 28 x^{2} - 254$ $-\,2^{11}\cdot 127$ $D_{4}$ (as 4T3) $[2]$ $16.1916332347$
4.2.325632.1 $x^{4} + 8 x^{2} - 32 x + 8$ $-\,2^{11}\cdot 3\cdot 53$ $S_4$ (as 4T5) $[4]$ $15.4064476049$
4.4.329728.1 $x^{4} - 36 x^{2} + 322$ $2^{11}\cdot 7\cdot 23$ $D_{4}$ (as 4T3) $[2]$ $26.8667897328$
4.0.329728.2 $x^{4} + 44 x^{2} + 322$ $2^{11}\cdot 7\cdot 23$ $D_{4}$ (as 4T3) $[2, 6]$ $1.76274717404$
4.2.358400.1 $x^{4} - 20 x^{2} - 350$ $-\,2^{11}\cdot 5^{2}\cdot 7$ $D_{4}$ (as 4T3) $[2, 2]$ $8.13843459956$
4.2.391168.2 $x^{4} + 28 x^{2} - 382$ $-\,2^{11}\cdot 191$ $D_{4}$ (as 4T3) $[2]$ $13.6686699585$
4.0.395264.1 $x^{4} + 44 x^{2} + 386$ $2^{11}\cdot 193$ $D_{4}$ (as 4T3) $[8]$ $1.76274717404$
4.2.423936.2 $x^{4} + 12 x^{2} - 414$ $-\,2^{11}\cdot 3^{2}\cdot 23$ $D_{4}$ (as 4T3) $[2]$ $15.9526701329$
4.2.456704.1 $x^{4} - 4 x^{2} - 446$ $-\,2^{11}\cdot 223$ $D_{4}$ (as 4T3) $[2]$ $12.0408395708$
4.0.460800.2 $x^{4} + 60 x^{2} + 450$ $2^{11}\cdot 3^{2}\cdot 5^{2}$ $C_4$ (as 4T1) $[2, 10]$ $1.76274717404$
4.2.489472.1 $x^{4} - 20 x^{2} - 478$ $-\,2^{11}\cdot 239$ $D_{4}$ (as 4T3) $[4]$ $6.66050024543$
4.0.493568.1 $x^{4} + 44 x^{2} + 482$ $2^{11}\cdot 241$ $D_{4}$ (as 4T3) $[12]$ $1.76274717404$
4.4.526336.1 $x^{4} - 52 x^{2} + 514$ $2^{11}\cdot 257$ $D_{4}$ (as 4T3) $[2]$ $32.8571414649$
4.2.555008.1 $x^{4} + 8 x^{2} - 8 x - 2$ $-\,2^{11}\cdot 271$ $S_4$ (as 4T5) $[4]$ $18.0650718326$
4.2.555008.4 $x^{4} + 12 x^{2} - 542$ $-\,2^{11}\cdot 271$ $D_{4}$ (as 4T3) $[2]$ $13.1443513809$
4.2.587776.1 $x^{4} - 4 x^{2} - 574$ $-\,2^{11}\cdot 7\cdot 41$ $D_{4}$ (as 4T3) $[2, 2]$ $12.8741350311$
4.2.587776.4 $x^{4} + 44 x^{2} - 574$ $-\,2^{11}\cdot 7\cdot 41$ $D_{4}$ (as 4T3) $[2, 2]$ $7.18012571619$
4.0.591872.1 $x^{4} + 12 x^{2} + 2$ $2^{11}\cdot 17^{2}$ $D_{4}$ (as 4T3) $[2, 4]$ $8.49658219583$
4.4.591872.2 $x^{4} - 68 x^{2} + 578$ $2^{11}\cdot 17^{2}$ $C_4$ (as 4T1) $[2]$ $37.5971712755$
4.2.686080.1 $x^{4} - 8 x^{2} - 8 x + 30$ $-\,2^{11}\cdot 5\cdot 67$ $S_4$ (as 4T5) $[4]$ $34.3284638726$
4.4.690176.1 $x^{4} - 52 x^{2} + 674$ $2^{11}\cdot 337$ $D_{4}$ (as 4T3) $[4]$ $20.3260981796$
4.4.722944.1 $x^{4} - 68 x^{2} + 706$ $2^{11}\cdot 353$ $D_{4}$ (as 4T3) $[2]$ $34.7023674652$
4.2.751616.2 $x^{4} - 36 x^{2} - 734$ $-\,2^{11}\cdot 367$ $D_{4}$ (as 4T3) $[2]$ $22.8017898517$
4.0.755712.3 $x^{4} + 60 x^{2} + 738$ $2^{11}\cdot 3^{2}\cdot 41$ $D_{4}$ (as 4T3) $[2, 6]$ $1.76274717404$
4.2.784384.4 $x^{4} + 44 x^{2} - 766$ $-\,2^{11}\cdot 383$ $D_{4}$ (as 4T3) $[4]$ $14.170989315$
4.0.821248.3 $x^{4} + 60 x^{2} + 802$ $2^{11}\cdot 401$ $D_{4}$ (as 4T3) $[12]$ $1.76274717404$
4.2.882688.2 $x^{4} + 28 x^{2} - 862$ $-\,2^{11}\cdot 431$ $D_{4}$ (as 4T3) $[4]$ $11.8498830765$
4.0.886784.1 $x^{4} + 76 x^{2} + 866$ $2^{11}\cdot 433$ $D_{4}$ (as 4T3) $[20]$ $1.76274717404$
4.0.903168.2 $x^{4} + 12 x^{2} + 162$ $2^{11}\cdot 3^{2}\cdot 7^{2}$ $D_{4}$ (as 4T3) $[2, 4]$ $12.9367607778$
4.0.919552.2 $x^{4} + 60 x^{2} + 898$ $2^{11}\cdot 449$ $D_{4}$ (as 4T3) $[24]$ $1.76274717404$
4.0.919552.4 $x^{4} + 20 x^{2} - 16 x + 60$ $2^{11}\cdot 449$ $S_4$ (as 4T5) $[4]$ $21.406024154$
4.2.948224.1 $x^{4} - 36 x^{2} - 926$ $-\,2^{11}\cdot 463$ $D_{4}$ (as 4T3) $[4]$ $16.3793341001$
4.2.964608.2 $x^{4} - 8 x^{2} - 72 x - 2$ $-\,2^{11}\cdot 3\cdot 157$ $S_4$ (as 4T5) $[4]$ $37.66496207$
4.2.980992.2 $x^{4} - 20 x^{2} - 958$ $-\,2^{11}\cdot 479$ $D_{4}$ (as 4T3) $[2]$ $28.4907023005$
4.2.997376.8 $x^{4} + 12 x^{2} - 64 x - 30$ $-\,2^{11}\cdot 487$ $S_4$ (as 4T5) $[4]$ $51.3664411957$
4.0.1017856.2 $x^{4} + 76 x^{2} + 994$ $2^{11}\cdot 7\cdot 71$ $D_{4}$ (as 4T3) $[2, 14]$ $1.76274717404$
4.4.1017856.2 $x^{4} - 68 x^{2} + 994$ $2^{11}\cdot 7\cdot 71$ $D_{4}$ (as 4T3) $[2]$ $37.3706159382$
4.2.1046528.3 $x^{4} + 12 x^{2} - 1022$ $-\,2^{11}\cdot 7\cdot 73$ $D_{4}$ (as 4T3) $[2]$ $33.6787824538$
4.2.1046528.4 $x^{4} + 60 x^{2} - 1022$ $-\,2^{11}\cdot 7\cdot 73$ $D_{4}$ (as 4T3) $[2]$ $20.5191889547$
4.0.1050624.1 $x^{4} + 12 x^{2} - 64 x + 66$ $2^{11}\cdot 3^{3}\cdot 19$ $S_4$ (as 4T5) $[8]$ $12.5169924053$
4.2.1079296.2 $x^{4} - 4 x^{2} - 1054$ $-\,2^{11}\cdot 17\cdot 31$ $D_{4}$ (as 4T3) $[4]$ $14.7571657282$
Next   To download results, determine the number of results.