| 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 |
| 4.4.39605.1 |
$x^{4} - 2 x^{3} - 8 x^{2} + 9 x - 2$ |
$4$ |
[4,0] |
$5\cdot 89^{2}$ |
$2$ |
$14.1070921879$ |
$21.095023109728988$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$29.635899035$ |
| 4.0.71289.1 |
$x^{4} - x^{3} + 23 x^{2} + 22 x + 484$ |
$4$ |
[0,2] |
$3^{2}\cdot 89^{2}$ |
$2$ |
$16.3401346384$ |
$16.34013463836819$ |
✓ |
✓ |
|
$C_2^2$ (as 4T2) |
trivial |
$6$ |
$1$ |
$13.815512558$ |
| 4.0.134657.1 |
$x^{4} - x^{3} - 6 x^{2} - 8 x + 64$ |
$4$ |
[0,2] |
$17\cdot 89^{2}$ |
$2$ |
$19.1561060939$ |
$38.897300677553446$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[7]$ |
$2$ |
$1$ |
$13.815512558$ |
| 4.2.158420.1 |
$x^{4} - 3 x^{2} - 20$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 5\cdot 89^{2}$ |
$3$ |
$19.9504410978$ |
$42.190046219457976$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$2$ |
$15.2596750374$ |
| 4.2.158420.2 |
$x^{4} + 3 x^{2} - 20$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 5\cdot 89^{2}$ |
$3$ |
$19.9504410978$ |
$42.190046219457976$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$2$ |
$40.2202711165$ |
| 4.2.285156.1 |
$x^{4} - x^{3} - 7 x^{2} + 37 x + 34$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 3^{2}\cdot 89^{2}$ |
$3$ |
$23.1084400166$ |
$32.68026927673638$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$94.9008509343$ |
| 4.2.316840.1 |
$x^{4} - 7 x^{2} - 10$ |
$4$ |
[2,1] |
$-\,2^{3}\cdot 5\cdot 89^{2}$ |
$3$ |
$23.7252065009$ |
$59.665735560705194$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$2$ |
$57.2967329675$ |
| 4.2.316840.2 |
$x^{4} + 14 x^{2} - 40$ |
$4$ |
[2,1] |
$-\,2^{3}\cdot 5\cdot 89^{2}$ |
$3$ |
$23.7252065009$ |
$59.665735560705194$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$2$ |
$28.8889699176$ |
| 4.0.316840.1 |
$x^{4} - x^{3} - 4 x^{2} - 9 x + 81$ |
$4$ |
[0,2] |
$2^{3}\cdot 5\cdot 89^{2}$ |
$3$ |
$23.7252065009$ |
$59.665735560705194$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$1$ |
$13.815512558$ |
| 4.0.316840.2 |
$x^{4} - x^{3} - 3 x^{2} + 35 x + 68$ |
$4$ |
[0,2] |
$2^{3}\cdot 5\cdot 89^{2}$ |
$3$ |
$23.7252065009$ |
$59.665735560705194$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[8]$ |
$2$ |
$1$ |
$13.815512558$ |
| 4.2.372287.1 |
$x^{4} - x^{3} - 9 x^{2} + 38 x + 20$ |
$4$ |
[2,1] |
$-\,47\cdot 89^{2}$ |
$2$ |
$24.7012805222$ |
$64.67611614808051$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$39.8972257052$ |
| 4.0.388129.1 |
$x^{4} - 41 x^{2} + 576$ |
$4$ |
[0,2] |
$7^{2}\cdot 89^{2}$ |
$2$ |
$24.9599679487$ |
$24.95996794869737$ |
✓ |
✓ |
|
$C_2^2$ (as 4T2) |
$[11]$ |
$2$ |
$1$ |
$13.815512558$ |
| 4.0.419813.1 |
$x^{4} - 2 x^{3} + 22 x^{2} - 21 x + 88$ |
$4$ |
[0,2] |
$53\cdot 89^{2}$ |
$2$ |
$25.4544648372$ |
$68.6804193347711$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[5]$ |
$2$ |
$1$ |
$13.815512558$ |
| 4.2.435655.1 |
$x^{4} - 2 x^{3} + 5 x^{2} - 4 x - 85$ |
$4$ |
[2,1] |
$-\,5\cdot 11\cdot 89^{2}$ |
$3$ |
$25.6912760553$ |
$69.96427659884722$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$2$ |
$20.4771096545$ |
| 4.2.435655.2 |
$x^{4} - 2 x^{3} - 17 x^{2} + 18 x - 8$ |
$4$ |
[2,1] |
$-\,5\cdot 11\cdot 89^{2}$ |
$3$ |
$25.6912760553$ |
$69.96427659884722$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$2$ |
$135.489661067$ |
| 4.2.538628.1 |
$x^{4} - x^{3} - 5 x^{2} + 36 x + 50$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 17\cdot 89^{2}$ |
$3$ |
$27.0908250402$ |
$77.79460135510689$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$74.1972259319$ |
| 4.2.538628.2 |
$x^{4} - x^{3} - 10 x^{2} + 83 x - 53$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 17\cdot 89^{2}$ |
$3$ |
$27.0908250402$ |
$77.79460135510689$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$58.193544967$ |
| 4.2.562391.1 |
$x^{4} - x^{3} - 19 x^{2} - 46 x - 20$ |
$4$ |
[2,1] |
$-\,71\cdot 89^{2}$ |
$2$ |
$27.3848010731$ |
$79.4921379760288$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$64.7627460933$ |
| 4.2.570312.1 |
$x^{4} - 27 x^{2} - 18$ |
$4$ |
[2,1] |
$-\,2^{3}\cdot 3^{2}\cdot 89^{2}$ |
$3$ |
$27.4807212843$ |
$46.216880033165374$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$76.4386802685$ |
| 4.4.570312.1 |
$x^{4} - x^{3} - 19 x^{2} + 43 x - 20$ |
$4$ |
[4,0] |
$2^{3}\cdot 3^{2}\cdot 89^{2}$ |
$3$ |
$27.4807212843$ |
$46.216880033165374$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$239.9003612$ |
| 4.2.625759.1 |
$x^{4} - x^{3} - 3 x^{2} - 54 x + 68$ |
$4$ |
[2,1] |
$-\,79\cdot 89^{2}$ |
$2$ |
$28.1255987161$ |
$83.85105843100611$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$31.3219052649$ |
| 4.0.633680.1 |
$x^{4} + 13 x^{2} + 20$ |
$4$ |
[0,2] |
$2^{4}\cdot 5\cdot 89^{2}$ |
$3$ |
$28.2141843758$ |
$42.190046219457976$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[2, 2]$ |
$2$ |
$1$ |
$13.815512558$ |
| 4.0.641601.1 |
$x^{4} - x^{3} - 11 x + 32$ |
$4$ |
[0,2] |
$3^{4}\cdot 89^{2}$ |
$2$ |
$28.3019433962$ |
$40.818465701990505$ |
|
|
|
$A_4$ (as 4T4) |
$[2]$ |
$2$ |
$1$ |
$32.7129196842$ |
| 4.2.784179.1 |
$x^{4} - 2 x^{3} - 12 x^{2} + 13 x - 158$ |
$4$ |
[2,1] |
$-\,3^{2}\cdot 11\cdot 89^{2}$ |
$3$ |
$29.758004285$ |
$54.194095619356915$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$183.624080598$ |
| 4.2.847547.1 |
$x^{4} - 2 x^{3} - 10 x^{2} + 11 x - 170$ |
$4$ |
[2,1] |
$-\,89^{2}\cdot 107$ |
$2$ |
$30.3417725013$ |
$97.58585963140357$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$144.874233461$ |
| 4.0.863389.1 |
$x^{4} - x^{3} + 5 x^{2} - 58 x + 160$ |
$4$ |
[0,2] |
$89^{2}\cdot 109$ |
$2$ |
$30.4825733706$ |
$98.49365461794989$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[11]$ |
$2$ |
$1$ |
$13.815512558$ |
| 4.2.1037651.1 |
$x^{4} - 2 x^{3} - 6 x^{2} + 7 x - 10$ |
$4$ |
[2,1] |
$-\,89^{2}\cdot 131$ |
$2$ |
$31.9163212113$ |
$107.97684937059425$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$218.043035379$ |
| 4.2.1077256.1 |
$x^{4} - x^{3} - 21 x^{2} - 45 x - 22$ |
$4$ |
[2,1] |
$-\,2^{3}\cdot 17\cdot 89^{2}$ |
$3$ |
$32.2166018891$ |
$110.01818031580054$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$156.821170717$ |
| 4.2.1077256.2 |
$x^{4} - x^{3} - 9 x^{2} - 51 x + 20$ |
$4$ |
[2,1] |
$-\,2^{3}\cdot 17\cdot 89^{2}$ |
$3$ |
$32.2166018891$ |
$110.01818031580054$ |
|
|
|
$D_{4}$ (as 4T3) |
$[3]$ |
$2$ |
$2$ |
$103.038072424$ |
| 4.4.1077256.1 |
$x^{4} - 15 x^{2} + 34$ |
$4$ |
[4,0] |
$2^{3}\cdot 17\cdot 89^{2}$ |
$3$ |
$32.2166018891$ |
$110.01818031580054$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$178.887884697$ |
| 4.4.1077256.2 |
$x^{4} - 30 x^{2} + 136$ |
$4$ |
[4,0] |
$2^{3}\cdot 17\cdot 89^{2}$ |
$3$ |
$32.2166018891$ |
$110.01818031580054$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$118.315755579$ |
| 4.0.1140624.1 |
$x^{4} + 43 x^{2} + 529$ |
$4$ |
[0,2] |
$2^{4}\cdot 3^{2}\cdot 89^{2}$ |
$3$ |
$32.6802692767$ |
$32.68026927673638$ |
✓ |
✓ |
|
$C_2^2$ (as 4T2) |
$[12]$ |
$2$ |
$1$ |
$2.63391579385$ |
| 4.4.1140624.1 |
$x^{4} - 2 x^{3} - 49 x^{2} + 50 x + 358$ |
$4$ |
[4,0] |
$2^{4}\cdot 3^{2}\cdot 89^{2}$ |
$3$ |
$32.6802692767$ |
$32.68026927673638$ |
|
✓ |
|
$C_2^2$ (as 4T2) |
trivial |
$2$ |
$3$ |
$154.238052988$ |
| 4.0.1140624.3 |
$x^{4} - 89 x^{2} + 7921$ |
$4$ |
[0,2] |
$2^{4}\cdot 3^{2}\cdot 89^{2}$ |
$3$ |
$32.6802692767$ |
$32.68026927673638$ |
✓ |
✓ |
|
$C_2^2$ (as 4T2) |
$[12]$ |
$6$ |
$1$ |
$16.9544082797$ |
| 4.0.1243597.1 |
$x^{4} - x^{3} + 2 x^{2} - 12 x + 144$ |
$4$ |
[0,2] |
$89^{2}\cdot 157$ |
$2$ |
$33.3941133086$ |
$118.20744477400736$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[9]$ |
$2$ |
$1$ |
$13.815512558$ |
| 4.2.1267360.1 |
$x^{4} - 14 x^{2} - 40$ |
$4$ |
[2,1] |
$-\,2^{5}\cdot 5\cdot 89^{2}$ |
$3$ |
$33.5525088037$ |
$84.38009243891595$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$2$ |
$69.1751460708$ |
| 4.2.1267360.2 |
$x^{4} + 7 x^{2} - 10$ |
$4$ |
[2,1] |
$-\,2^{5}\cdot 5\cdot 89^{2}$ |
$3$ |
$33.5525088037$ |
$84.38009243891595$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$2$ |
$41.6509474459$ |
| 4.4.1267360.1 |
$x^{4} - 29 x^{2} + 10$ |
$4$ |
[4,0] |
$2^{5}\cdot 5\cdot 89^{2}$ |
$3$ |
$33.5525088037$ |
$84.38009243891595$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$3$ |
$131.771432968$ |
| 4.4.1267360.2 |
$x^{4} - 27 x^{2} + 160$ |
$4$ |
[4,0] |
$2^{5}\cdot 5\cdot 89^{2}$ |
$3$ |
$33.5525088037$ |
$84.38009243891595$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$3$ |
$97.7978312634$ |
| 4.4.1338649.1 |
$x^{4} - 51 x^{2} + 361$ |
$4$ |
[4,0] |
$13^{2}\cdot 89^{2}$ |
$2$ |
$34.0147027034$ |
$34.0147027033899$ |
|
✓ |
|
$C_2^2$ (as 4T2) |
trivial |
$2$ |
$3$ |
$69.6518860874$ |
| 4.4.1370333.1 |
$x^{4} - 2 x^{3} - 10 x^{2} + 11 x + 8$ |
$4$ |
[4,0] |
$89^{2}\cdot 173$ |
$2$ |
$34.2142109799$ |
$124.08464852672147$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$261.581041285$ |
| 4.2.1481227.1 |
$x^{4} - x^{3} - 20 x^{2} + 88 x - 88$ |
$4$ |
[2,1] |
$-\,11\cdot 17\cdot 89^{2}$ |
$3$ |
$34.8863396686$ |
$129.00775170508166$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$190.006175022$ |
| 4.2.1481227.2 |
$x^{4} - 2 x^{3} + 8 x^{2} - 7 x - 10$ |
$4$ |
[2,1] |
$-\,11\cdot 17\cdot 89^{2}$ |
$3$ |
$34.8863396686$ |
$129.00775170508166$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$177.975004179$ |
| 4.0.1489148.1 |
$x^{4} + 29 x^{2} + 188$ |
$4$ |
[0,2] |
$2^{2}\cdot 47\cdot 89^{2}$ |
$3$ |
$34.9328859225$ |
$129.35223229616102$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[10]$ |
$2$ |
$1$ |
$13.815512558$ |
| 4.4.1489148.1 |
$x^{4} - x^{3} - 18 x^{2} - 2 x + 4$ |
$4$ |
[4,0] |
$2^{2}\cdot 47\cdot 89^{2}$ |
$3$ |
$34.9328859225$ |
$129.35223229616102$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$418.613514652$ |
| 4.0.1497069.1 |
$x^{4} - x^{3} + 201 x^{2} - 67 x + 10363$ |
$4$ |
[0,2] |
$3^{3}\cdot 7\cdot 89^{2}$ |
$3$ |
$34.9792468551$ |
$56.89642308042072$ |
|
|
|
$D_{4}$ (as 4T3) |
$[14]$ |
$6$ |
$1$ |
$8.95519875203$ |
| 4.2.1552516.1 |
$x^{4} - x^{3} - 2 x^{2} + 79 x + 11$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 7^{2}\cdot 89^{2}$ |
$3$ |
$35.2987251894$ |
$49.91993589739474$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$67.3565382305$ |
| 4.2.1576279.1 |
$x^{4} - 2 x^{3} + 19 x^{2} - 18 x - 8$ |
$4$ |
[2,1] |
$-\,89^{2}\cdot 199$ |
$2$ |
$35.4330284084$ |
$133.08268106707197$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$384.523087695$ |
| 4.2.1679252.1 |
$x^{4} - 12 x^{2} - 53$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 53\cdot 89^{2}$ |
$3$ |
$35.9980493957$ |
$137.3608386695422$ |
|
|
|
$D_{4}$ (as 4T3) |
$[3]$ |
$2$ |
$2$ |
$117.564371557$ |
| 4.2.1679252.2 |
$x^{4} + 12 x^{2} - 53$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 53\cdot 89^{2}$ |
$3$ |
$35.9980493957$ |
$137.3608386695422$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$130.858357811$ |
