Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
4.2.448.1 |
$x^{4} - 2 x^{3} + x^{2} - 2 x + 1$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 7$ |
$2$ |
$4.60065326758$ |
$7.483314773547883$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$0.557886846205$ |
4.0.576.2 |
$x^{4} + 2 x^{2} + 4$ |
$4$ |
[0,2] |
$2^{6}\cdot 3^{2}$ |
$2$ |
$4.89897948557$ |
$4.898979485566356$ |
✓ |
✓ |
|
$C_2^2$ (as 4T2) |
trivial |
$6$ |
$1$ |
$1.76274717404$ |
4.2.1472.2 |
$x^{4} - 2 x^{3} + 3 x^{2} - 2 x - 1$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 23$ |
$2$ |
$6.19408202936$ |
$13.564659966250536$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$1.25951480215$ |
4.4.1600.1 |
$x^{4} - 6 x^{2} + 4$ |
$4$ |
[4,0] |
$2^{6}\cdot 5^{2}$ |
$2$ |
$6.32455532034$ |
$6.324555320336759$ |
|
✓ |
|
$C_2^2$ (as 4T2) |
trivial |
$2$ |
$3$ |
$1.54250590983$ |
4.4.2624.1 |
$x^{4} - 2 x^{3} - 3 x^{2} + 2 x + 1$ |
$4$ |
[4,0] |
$2^{6}\cdot 41$ |
$2$ |
$7.15716381673$ |
$18.110770276274835$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$2.18595620669$ |
4.2.4544.1 |
$x^{4} - 2 x^{3} + x^{2} - 6 x - 1$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 71$ |
$2$ |
$8.21031048045$ |
$23.83275057562597$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$2.44416015518$ |
4.0.4672.2 |
$x^{4} - 2 x^{3} + 5 x^{2} - 2 x + 7$ |
$4$ |
[0,2] |
$2^{6}\cdot 73$ |
$2$ |
$8.26752864903$ |
$24.166091947189145$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$1$ |
$1.76274717404$ |
4.0.5696.1 |
$x^{4} - 2 x^{3} + 7 x^{2} - 6 x + 7$ |
$4$ |
[0,2] |
$2^{6}\cdot 89$ |
$2$ |
$8.68745354269$ |
$26.68332812825267$ |
✓ |
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$1$ |
$1.76274717404$ |
4.2.6592.1 |
$x^{4} - 2 x^{3} - x^{2} + 2 x - 7$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 103$ |
$2$ |
$9.01061221676$ |
$28.705400188814647$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$3.19105476131$ |
4.2.7616.1 |
$x^{4} - 2 x^{3} + 3 x^{2} - 2 x - 7$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 7\cdot 17$ |
$3$ |
$9.34182513843$ |
$30.854497241083024$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$3.45560630835$ |
4.2.7616.2 |
$x^{4} - 2 x^{3} + 5 x^{2} + 6 x - 9$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 7\cdot 17$ |
$3$ |
$9.34182513843$ |
$30.854497241083024$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$3.05293335278$ |
4.0.7744.2 |
$x^{4} - 2 x^{3} + 3 x^{2} - 2 x + 23$ |
$4$ |
[0,2] |
$2^{6}\cdot 11^{2}$ |
$2$ |
$9.38083151965$ |
$9.38083151964686$ |
✓ |
✓ |
|
$C_2^2$ (as 4T2) |
trivial |
$2$ |
$1$ |
$1.76274717404$ |
4.4.8768.1 |
$x^{4} - 2 x^{3} - 5 x^{2} + 6 x + 7$ |
$4$ |
[4,0] |
$2^{6}\cdot 137$ |
$2$ |
$9.67665227678$ |
$33.1058907144937$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$4.92588435923$ |
4.2.9664.1 |
$x^{4} - 2 x^{3} - 3 x^{2} - 6 x - 7$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 151$ |
$2$ |
$9.91492036375$ |
$34.75629439396553$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$3.4305294243$ |
4.4.9792.1 |
$x^{4} - 2 x^{3} - 7 x^{2} + 2 x + 7$ |
$4$ |
[4,0] |
$2^{6}\cdot 3^{2}\cdot 17$ |
$3$ |
$9.94758940723$ |
$20.199009876724155$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$4.9482532611$ |
4.2.10688.1 |
$x^{4} - 2 x^{3} + 7 x^{2} - 6 x - 9$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 167$ |
$2$ |
$10.167732484$ |
$36.55133376499413$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$4.5056685074$ |
4.4.10816.1 |
$x^{4} - 2 x^{3} - 9 x^{2} + 10 x - 1$ |
$4$ |
[4,0] |
$2^{6}\cdot 13^{2}$ |
$2$ |
$10.1980390272$ |
$10.198039027185569$ |
|
✓ |
|
$C_2^2$ (as 4T2) |
trivial |
$2$ |
$3$ |
$4.87014657656$ |
4.2.12736.2 |
$x^{4} - 2 x^{3} + x^{2} - 10 x - 7$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 199$ |
$2$ |
$10.6232710517$ |
$39.89987468652001$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$4.59111047401$ |
4.0.13888.1 |
$x^{4} - 2 x^{3} + 9 x^{2} - 2 x + 17$ |
$4$ |
[0,2] |
$2^{6}\cdot 7\cdot 31$ |
$3$ |
$10.8557523416$ |
$41.66533331199932$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$1$ |
$1.76274717404$ |
4.4.13888.1 |
$x^{4} - 2 x^{3} - 7 x^{2} + 6 x + 9$ |
$4$ |
[4,0] |
$2^{6}\cdot 7\cdot 31$ |
$3$ |
$10.8557523416$ |
$41.66533331199932$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$6.51385459818$ |
4.0.14400.5 |
$x^{4} - 2 x^{3} + 11 x^{2} - 10 x + 55$ |
$4$ |
[0,2] |
$2^{6}\cdot 3^{2}\cdot 5^{2}$ |
$3$ |
$10.9544511501$ |
$10.954451150103322$ |
✓ |
✓ |
|
$C_2^2$ (as 4T2) |
$[4]$ |
$2$ |
$1$ |
$0.962423650119$ |
4.0.14400.7 |
$x^{4} + 10 x^{2} + 100$ |
$4$ |
[0,2] |
$2^{6}\cdot 3^{2}\cdot 5^{2}$ |
$3$ |
$10.9544511501$ |
$10.954451150103322$ |
✓ |
✓ |
|
$C_2^2$ (as 4T2) |
$[4]$ |
$6$ |
$1$ |
$3.63689291846$ |
4.0.14912.2 |
$x^{4} - 2 x^{3} + 11 x^{2} - 10 x + 17$ |
$4$ |
[0,2] |
$2^{6}\cdot 233$ |
$2$ |
$11.0505520305$ |
$43.174066289845804$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$1$ |
$1.76274717404$ |
4.2.16832.1 |
$x^{4} - 2 x^{3} - x^{2} + 2 x - 17$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 263$ |
$2$ |
$11.3902676844$ |
$45.86937976471886$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$5.04791146145$ |
4.2.17856.3 |
$x^{4} - 2 x^{3} + 3 x^{2} - 2 x - 17$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 3^{2}\cdot 31$ |
$3$ |
$11.5596861855$ |
$27.27636339397171$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$3.89903914047$ |
4.0.17984.1 |
$x^{4} - 2 x^{3} + 9 x^{2} - 6 x + 23$ |
$4$ |
[0,2] |
$2^{6}\cdot 281$ |
$2$ |
$11.5803470118$ |
$47.41307836451879$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$1$ |
$1.76274717404$ |
4.0.19008.2 |
$x^{4} - 12 x + 15$ |
$4$ |
[0,2] |
$2^{6}\cdot 3^{3}\cdot 11$ |
$3$ |
$11.7417845116$ |
$21.383671649138826$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$1$ |
$3.2893017342$ |
4.2.19904.1 |
$x^{4} - 2 x^{3} + 5 x^{2} + 10 x - 23$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 311$ |
$2$ |
$11.8777749056$ |
$49.879855653359705$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$4.41592807007$ |
4.4.20032.1 |
$x^{4} - 2 x^{3} - 9 x^{2} + 10 x + 17$ |
$4$ |
[4,0] |
$2^{6}\cdot 313$ |
$2$ |
$11.8968251271$ |
$50.039984012787215$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$7.66160460504$ |
4.0.21056.1 |
$x^{4} - 2 x^{3} + 11 x^{2} - 10 x + 23$ |
$4$ |
[0,2] |
$2^{6}\cdot 7\cdot 47$ |
$3$ |
$12.0460307644$ |
$51.30302135352264$ |
✓ |
|
✓ |
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$1$ |
$1.76274717404$ |
4.4.21056.1 |
$x^{4} - 2 x^{3} - 11 x^{2} + 2 x + 17$ |
$4$ |
[4,0] |
$2^{6}\cdot 7\cdot 47$ |
$3$ |
$12.0460307644$ |
$51.30302135352264$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$7.80084455155$ |
4.2.22976.1 |
$x^{4} - 2 x^{3} + 9 x^{2} + 10 x - 25$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 359$ |
$2$ |
$12.3117164755$ |
$53.59104402789705$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$5.76315689585$ |
4.0.23104.3 |
$x^{4} - 2 x^{3} + 7 x^{2} - 6 x + 47$ |
$4$ |
[0,2] |
$2^{6}\cdot 19^{2}$ |
$2$ |
$12.3288280059$ |
$12.328828005937952$ |
✓ |
✓ |
|
$C_2^2$ (as 4T2) |
$[3]$ |
$2$ |
$1$ |
$1.76274717404$ |
4.2.24000.1 |
$x^{4} - 2 x^{3} - x^{2} + 2 x - 9$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 3\cdot 5^{3}$ |
$3$ |
$12.4466595458$ |
$16.3807251762544$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$2$ |
$6.51369983407$ |
4.2.25024.1 |
$x^{4} - 2 x^{3} + x^{2} - 14 x - 17$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 17\cdot 23$ |
$3$ |
$12.5773510512$ |
$55.92852581643825$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$4.1552875885$ |
4.2.25024.2 |
$x^{4} - 2 x^{3} + 7 x^{2} - 6 x - 23$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 17\cdot 23$ |
$3$ |
$12.5773510512$ |
$55.92852581643825$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$6.49256732077$ |
4.4.26176.1 |
$x^{4} - 2 x^{3} - 9 x^{2} + 10 x + 23$ |
$4$ |
[4,0] |
$2^{6}\cdot 409$ |
$2$ |
$12.719669309$ |
$57.201398584300364$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$8.8297151471$ |
4.2.27072.3 |
$x^{4} - 2 x^{3} - 7 x^{2} - 10 x - 23$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 3^{2}\cdot 47$ |
$3$ |
$12.8271473995$ |
$33.58571124749333$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$4.82233582041$ |
4.0.27200.2 |
$x^{4} - 2 x^{3} + 13 x^{2} - 2 x + 31$ |
$4$ |
[0,2] |
$2^{6}\cdot 5^{2}\cdot 17$ |
$3$ |
$12.842282703$ |
$26.076809620810597$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$1$ |
$1.76274717404$ |
4.2.28096.2 |
$x^{4} - 2 x^{3} + 11 x^{2} - 10 x - 25$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 439$ |
$2$ |
$12.9467607809$ |
$59.262129560116215$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$4.28079126943$ |
4.0.28224.1 |
$x^{4} + 10 x^{2} + 4$ |
$4$ |
[0,2] |
$2^{6}\cdot 3^{2}\cdot 7^{2}$ |
$3$ |
$12.9614813968$ |
$12.96148139681572$ |
✓ |
✓ |
|
$C_2^2$ (as 4T2) |
$[4]$ |
$2$ |
$1$ |
$3.13359847394$ |
4.4.28224.2 |
$x^{4} - 2 x^{3} - 13 x^{2} + 14 x + 7$ |
$4$ |
[4,0] |
$2^{6}\cdot 3^{2}\cdot 7^{2}$ |
$3$ |
$12.9614813968$ |
$12.96148139681572$ |
|
✓ |
|
$C_2^2$ (as 4T2) |
trivial |
$2$ |
$3$ |
$8.99434740307$ |
4.0.28224.5 |
$x^{4} - 14 x^{2} + 196$ |
$4$ |
[0,2] |
$2^{6}\cdot 3^{2}\cdot 7^{2}$ |
$3$ |
$12.9614813968$ |
$12.96148139681572$ |
✓ |
✓ |
|
$C_2^2$ (as 4T2) |
$[4]$ |
$6$ |
$1$ |
$6.5132279096$ |
4.4.29248.1 |
$x^{4} - 2 x^{3} - 11 x^{2} + 6 x + 23$ |
$4$ |
[4,0] |
$2^{6}\cdot 457$ |
$2$ |
$13.0774793677$ |
$60.4648658313239$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$8.2189114846$ |
4.2.31168.1 |
$x^{4} - 2 x^{3} - x^{2} + 2 x - 31$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 487$ |
$2$ |
$13.2870091415$ |
$62.41794613730894$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$5.86421849873$ |
4.2.32192.3 |
$x^{4} - 2 x^{3} + 3 x^{2} - 2 x - 31$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 503$ |
$2$ |
$13.394823326$ |
$63.43500610861482$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$5.5619649932$ |
4.0.32832.3 |
$x^{4} - 30 x^{2} + 228$ |
$4$ |
[0,2] |
$2^{6}\cdot 3^{3}\cdot 19$ |
$3$ |
$13.4609073411$ |
$28.103650443517264$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$6$ |
$1$ |
$6.87232328207$ |
4.4.33344.1 |
$x^{4} - 2 x^{3} - 11 x^{2} + 10 x + 25$ |
$4$ |
[4,0] |
$2^{6}\cdot 521$ |
$2$ |
$13.5130823785$ |
$64.5600495662759$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$9.23513493428$ |
4.0.35392.1 |
$x^{4} - 2 x^{3} + 13 x^{2} - 6 x + 41$ |
$4$ |
[0,2] |
$2^{6}\cdot 7\cdot 79$ |
$3$ |
$13.7159620975$ |
$66.51315659326356$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$1$ |
$1.76274717404$ |
4.4.35392.1 |
$x^{4} - 2 x^{3} - 13 x^{2} + 14 x + 31$ |
$4$ |
[4,0] |
$2^{6}\cdot 7\cdot 79$ |
$3$ |
$13.7159620975$ |
$66.51315659326356$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$11.5035438122$ |