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 |
2.2.13.1 |
$x^{2} - x - 3$ |
$2$ |
[2,0] |
$13$ |
$1$ |
$3.60555127546$ |
$3.605551275463989$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$1.19476321729$ |
2.0.39.1 |
$x^{2} - x + 10$ |
$2$ |
[0,1] |
$-\,3\cdot 13$ |
$2$ |
$6.2449979984$ |
$6.244997998398398$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[4]$ |
$2$ |
0 |
$1$ |
2.0.52.1 |
$x^{2} + 13$ |
$2$ |
[0,1] |
$-\,2^{2}\cdot 13$ |
$2$ |
$7.21110255093$ |
$7.211102550927978$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
0 |
$1$ |
2.2.156.1 |
$x^{2} - 39$ |
$2$ |
[2,0] |
$2^{2}\cdot 3\cdot 13$ |
$3$ |
$12.4899959968$ |
$12.489995996796797$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$3.91162276521$ |
2.2.221.1 |
$x^{2} - x - 55$ |
$2$ |
[2,0] |
$13\cdot 17$ |
$2$ |
$14.8660687473$ |
$14.866068747318506$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$2.70357583093$ |
2.0.299.1 |
$x^{2} - x + 75$ |
$2$ |
[0,1] |
$-\,13\cdot 23$ |
$2$ |
$17.2916164658$ |
$17.291616465790582$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[8]$ |
$2$ |
0 |
$1$ |
2.2.377.1 |
$x^{2} - x - 94$ |
$2$ |
[2,0] |
$13\cdot 29$ |
$2$ |
$19.4164878389$ |
$19.4164878389476$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$6.14418102911$ |
2.0.455.1 |
$x^{2} - x + 114$ |
$2$ |
[0,1] |
$-\,5\cdot 7\cdot 13$ |
$3$ |
$21.3307290077$ |
$21.330729007701542$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 10]$ |
$2$ |
0 |
$1$ |
2.0.520.1 |
$x^{2} + 130$ |
$2$ |
[0,1] |
$-\,2^{3}\cdot 5\cdot 13$ |
$3$ |
$22.803508502$ |
$22.80350850198276$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 2]$ |
$2$ |
0 |
$1$ |
2.2.520.1 |
$x^{2} - 130$ |
$2$ |
[2,0] |
$2^{3}\cdot 5\cdot 13$ |
$3$ |
$22.803508502$ |
$22.80350850198276$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 2]$ |
$2$ |
$1$ |
$4.73627538627$ |
2.0.559.1 |
$x^{2} - x + 140$ |
$2$ |
[0,1] |
$-\,13\cdot 43$ |
$2$ |
$23.6431808351$ |
$23.643180835073778$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[16]$ |
$2$ |
0 |
$1$ |
2.0.663.1 |
$x^{2} - x + 166$ |
$2$ |
[0,1] |
$-\,3\cdot 13\cdot 17$ |
$3$ |
$25.7487863792$ |
$25.748786379167466$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 8]$ |
$2$ |
0 |
$1$ |
2.2.689.1 |
$x^{2} - x - 172$ |
$2$ |
[2,0] |
$13\cdot 53$ |
$2$ |
$26.2488094968$ |
$26.248809496813376$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[4]$ |
$2$ |
$1$ |
$5.34708485421$ |
2.0.715.1 |
$x^{2} - x + 179$ |
$2$ |
[0,1] |
$-\,5\cdot 11\cdot 13$ |
$3$ |
$26.7394839142$ |
$26.739483914241877$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 2]$ |
$2$ |
0 |
$1$ |
2.0.728.1 |
$x^{2} + 182$ |
$2$ |
[0,1] |
$-\,2^{3}\cdot 7\cdot 13$ |
$3$ |
$26.9814751265$ |
$26.981475126464083$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 6]$ |
$2$ |
0 |
$1$ |
2.2.728.1 |
$x^{2} - 182$ |
$2$ |
[2,0] |
$2^{3}\cdot 7\cdot 13$ |
$3$ |
$26.9814751265$ |
$26.981475126464083$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$3.98864093449$ |
2.2.793.1 |
$x^{2} - x - 198$ |
$2$ |
[2,0] |
$13\cdot 61$ |
$2$ |
$28.1602556807$ |
$28.160255680657446$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[4]$ |
$2$ |
$1$ |
$9.08091481158$ |
2.0.884.1 |
$x^{2} + 221$ |
$2$ |
[0,1] |
$-\,2^{2}\cdot 13\cdot 17$ |
$3$ |
$29.7321374946$ |
$29.732137494637012$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 8]$ |
$2$ |
0 |
$1$ |
2.2.897.1 |
$x^{2} - x - 224$ |
$2$ |
[2,0] |
$3\cdot 13\cdot 23$ |
$3$ |
$29.9499582637$ |
$29.949958263743873$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[4]$ |
$2$ |
$1$ |
$7.08840808191$ |
2.2.1001.1 |
$x^{2} - x - 250$ |
$2$ |
[2,0] |
$7\cdot 11\cdot 13$ |
$3$ |
$31.6385840391$ |
$31.63858403911275$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$14.567780056$ |
2.0.1027.1 |
$x^{2} - x + 257$ |
$2$ |
[0,1] |
$-\,13\cdot 79$ |
$2$ |
$32.0468407179$ |
$32.046840717924134$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[4]$ |
$2$ |
0 |
$1$ |
2.0.1131.1 |
$x^{2} - x + 283$ |
$2$ |
[0,1] |
$-\,3\cdot 13\cdot 29$ |
$3$ |
$33.6303434416$ |
$33.63034344160047$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 4]$ |
$2$ |
0 |
$1$ |
2.0.1144.1 |
$x^{2} + 286$ |
$2$ |
[0,1] |
$-\,2^{3}\cdot 11\cdot 13$ |
$3$ |
$33.8230690506$ |
$33.823069050575526$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 6]$ |
$2$ |
0 |
$1$ |
2.2.1144.1 |
$x^{2} - 286$ |
$2$ |
[2,0] |
$2^{3}\cdot 11\cdot 13$ |
$3$ |
$33.8230690506$ |
$33.823069050575526$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$13.932110672$ |
2.2.1196.1 |
$x^{2} - 299$ |
$2$ |
[2,0] |
$2^{2}\cdot 13\cdot 23$ |
$3$ |
$34.5832329316$ |
$34.583232931581165$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$6.7214242492$ |
2.0.1235.1 |
$x^{2} - x + 309$ |
$2$ |
[0,1] |
$-\,5\cdot 13\cdot 19$ |
$3$ |
$35.1425667816$ |
$35.14256678161116$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 6]$ |
$2$ |
0 |
$1$ |
2.2.1313.1 |
$x^{2} - x - 328$ |
$2$ |
[2,0] |
$13\cdot 101$ |
$2$ |
$36.235341864$ |
$36.235341863986875$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[4]$ |
$2$ |
$1$ |
$7.11639480293$ |
2.0.1339.1 |
$x^{2} - x + 335$ |
$2$ |
[0,1] |
$-\,13\cdot 103$ |
$2$ |
$36.5923489271$ |
$36.59234892706397$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[8]$ |
$2$ |
0 |
$1$ |
2.2.1365.1 |
$x^{2} - x - 341$ |
$2$ |
[2,0] |
$3\cdot 5\cdot 7\cdot 13$ |
$4$ |
$36.9459064038$ |
$36.945906403822335$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 2]$ |
$2$ |
$1$ |
$3.61018665079$ |
2.0.1391.1 |
$x^{2} - x + 348$ |
$2$ |
[0,1] |
$-\,13\cdot 107$ |
$2$ |
$37.2961123979$ |
$37.296112397943034$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[44]$ |
$2$ |
0 |
$1$ |
2.2.1469.1 |
$x^{2} - x - 367$ |
$2$ |
[2,0] |
$13\cdot 113$ |
$2$ |
$38.3275357935$ |
$38.3275357934736$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$4.74485650542$ |
2.0.1508.1 |
$x^{2} + 377$ |
$2$ |
[0,1] |
$-\,2^{2}\cdot 13\cdot 29$ |
$3$ |
$38.8329756779$ |
$38.8329756778952$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 8]$ |
$2$ |
0 |
$1$ |
2.0.1560.1 |
$x^{2} + 390$ |
$2$ |
[0,1] |
$-\,2^{3}\cdot 3\cdot 5\cdot 13$ |
$4$ |
$39.4968353163$ |
$39.496835316262995$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 2, 4]$ |
$2$ |
0 |
$1$ |
2.2.1560.1 |
$x^{2} - 390$ |
$2$ |
[2,0] |
$2^{3}\cdot 3\cdot 5\cdot 13$ |
$4$ |
$39.4968353163$ |
$39.496835316262995$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 2]$ |
$2$ |
$1$ |
$5.06255497294$ |
2.0.1651.1 |
$x^{2} - x + 413$ |
$2$ |
[0,1] |
$-\,13\cdot 127$ |
$2$ |
$40.6324993078$ |
$40.63249930782009$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[8]$ |
$2$ |
0 |
$1$ |
2.2.1677.1 |
$x^{2} - x - 419$ |
$2$ |
[2,0] |
$3\cdot 13\cdot 43$ |
$3$ |
$40.9511904589$ |
$40.95119045888654$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[4]$ |
$2$ |
$1$ |
$3.71297665117$ |
2.0.1703.1 |
$x^{2} - x + 426$ |
$2$ |
[0,1] |
$-\,13\cdot 131$ |
$2$ |
$41.2674205639$ |
$41.2674205639267$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[28]$ |
$2$ |
0 |
$1$ |
2.2.1729.1 |
$x^{2} - x - 432$ |
$2$ |
[2,0] |
$7\cdot 13\cdot 19$ |
$3$ |
$41.5812457726$ |
$41.58124577258358$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$32.122169485$ |
2.0.1807.1 |
$x^{2} - x + 452$ |
$2$ |
[0,1] |
$-\,13\cdot 139$ |
$2$ |
$42.5088226137$ |
$42.50882261366456$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[12]$ |
$2$ |
0 |
$1$ |
2.2.1820.1 |
$x^{2} - 455$ |
$2$ |
[2,0] |
$2^{2}\cdot 5\cdot 7\cdot 13$ |
$4$ |
$42.6614580154$ |
$42.661458015403085$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 2]$ |
$2$ |
$1$ |
$4.85196922317$ |
2.0.1976.1 |
$x^{2} + 494$ |
$2$ |
[0,1] |
$-\,2^{3}\cdot 13\cdot 19$ |
$3$ |
$44.4522215418$ |
$44.45222154178574$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 14]$ |
$2$ |
0 |
$1$ |
2.2.1976.1 |
$x^{2} - 494$ |
$2$ |
[2,0] |
$2^{3}\cdot 13\cdot 19$ |
$3$ |
$44.4522215418$ |
$44.45222154178574$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$11.8918412378$ |
2.0.2015.1 |
$x^{2} - x + 504$ |
$2$ |
[0,1] |
$-\,5\cdot 13\cdot 31$ |
$3$ |
$44.8887513749$ |
$44.88875137492688$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 26]$ |
$2$ |
0 |
$1$ |
2.2.2041.1 |
$x^{2} - x - 510$ |
$2$ |
[2,0] |
$13\cdot 157$ |
$2$ |
$45.1774279923$ |
$45.17742799230607$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$37.965028978$ |
2.0.2067.1 |
$x^{2} - x + 517$ |
$2$ |
[0,1] |
$-\,3\cdot 13\cdot 53$ |
$3$ |
$45.4642716867$ |
$45.46427168667722$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 4]$ |
$2$ |
0 |
$1$ |
2.2.2145.1 |
$x^{2} - x - 536$ |
$2$ |
[2,0] |
$3\cdot 5\cdot 11\cdot 13$ |
$4$ |
$46.3141447076$ |
$46.314144707637645$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 2]$ |
$2$ |
$1$ |
$10.9387694785$ |
2.0.2184.1 |
$x^{2} + 546$ |
$2$ |
[0,1] |
$-\,2^{3}\cdot 3\cdot 7\cdot 13$ |
$4$ |
$46.7332857822$ |
$46.73328578219169$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 2, 6]$ |
$2$ |
0 |
$1$ |
2.2.2184.1 |
$x^{2} - 546$ |
$2$ |
[2,0] |
$2^{3}\cdot 3\cdot 7\cdot 13$ |
$4$ |
$46.7332857822$ |
$46.73328578219169$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 2]$ |
$2$ |
$1$ |
$7.24565455884$ |
2.2.2236.1 |
$x^{2} - 559$ |
$2$ |
[2,0] |
$2^{2}\cdot 13\cdot 43$ |
$3$ |
$47.2863616701$ |
$47.286361670147556$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$20.7363168902$ |
2.2.2249.1 |
$x^{2} - x - 562$ |
$2$ |
[2,0] |
$13\cdot 173$ |
$2$ |
$47.4236228055$ |
$47.4236228055175$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[4]$ |
$2$ |
$1$ |
$12.8848165958$ |