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 |
2.0.47.1 |
$x^{2} - x + 12$ |
$2$ |
[0,1] |
$-\,47$ |
$1$ |
$6.8556546004$ |
$6.855654600401044$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[5]$ |
$2$ |
0 |
$1$ |
2.0.376.1 |
$x^{2} + 94$ |
$2$ |
[0,1] |
$-\,2^{3}\cdot 47$ |
$2$ |
$19.3907194297$ |
$19.390719429665317$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[8]$ |
$2$ |
0 |
$1$ |
2.2.517.1 |
$x^{2} - x - 129$ |
$2$ |
[2,0] |
$11\cdot 47$ |
$2$ |
$22.7376340018$ |
$22.737634001804146$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$9.26605885179$ |
2.0.564.1 |
$x^{2} + 141$ |
$2$ |
[0,1] |
$-\,2^{2}\cdot 3\cdot 47$ |
$3$ |
$23.7486841741$ |
$23.748684174075834$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 4]$ |
$2$ |
0 |
$1$ |
2.2.705.1 |
$x^{2} - x - 176$ |
$2$ |
[2,0] |
$3\cdot 5\cdot 47$ |
$3$ |
$26.5518360947$ |
$26.551836094703507$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$13.0696416949$ |
2.0.799.1 |
$x^{2} - x + 200$ |
$2$ |
[0,1] |
$-\,17\cdot 47$ |
$2$ |
$28.2665880502$ |
$28.26658805020514$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[16]$ |
$2$ |
0 |
$1$ |
2.2.893.1 |
$x^{2} - x - 223$ |
$2$ |
[2,0] |
$19\cdot 47$ |
$2$ |
$29.883105595$ |
$29.88310559496787$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$7.74109890116$ |
2.2.940.1 |
$x^{2} - 235$ |
$2$ |
[2,0] |
$2^{2}\cdot 5\cdot 47$ |
$3$ |
$30.6594194335$ |
$30.659419433511783$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[6]$ |
$2$ |
$1$ |
$4.52167040866$ |
2.0.987.1 |
$x^{2} - x + 247$ |
$2$ |
[0,1] |
$-\,3\cdot 7\cdot 47$ |
$3$ |
$31.4165561448$ |
$31.416556144810016$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 4]$ |
$2$ |
0 |
$1$ |
2.2.1081.1 |
$x^{2} - x - 270$ |
$2$ |
[2,0] |
$23\cdot 47$ |
$2$ |
$32.8785644455$ |
$32.87856444554719$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$47.8205851741$ |
2.0.1128.1 |
$x^{2} + 282$ |
$2$ |
[0,1] |
$-\,2^{3}\cdot 3\cdot 47$ |
$3$ |
$33.5857112475$ |
$33.58571124749333$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 4]$ |
$2$ |
0 |
$1$ |
2.0.1316.1 |
$x^{2} + 329$ |
$2$ |
[0,1] |
$-\,2^{2}\cdot 7\cdot 47$ |
$3$ |
$36.2767142944$ |
$36.27671429443411$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 12]$ |
$2$ |
0 |
$1$ |
2.2.1457.1 |
$x^{2} - x - 364$ |
$2$ |
[2,0] |
$31\cdot 47$ |
$2$ |
$38.170669368$ |
$38.17066936798463$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$30.3028446971$ |
2.2.1645.1 |
$x^{2} - x - 411$ |
$2$ |
[2,0] |
$5\cdot 7\cdot 47$ |
$3$ |
$40.5585995813$ |
$40.55859958134649$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$10.1904318515$ |
2.0.1739.1 |
$x^{2} - x + 435$ |
$2$ |
[0,1] |
$-\,37\cdot 47$ |
$2$ |
$41.701318924$ |
$41.701318923986086$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[20]$ |
$2$ |
0 |
$1$ |
2.2.1833.1 |
$x^{2} - x - 458$ |
$2$ |
[2,0] |
$3\cdot 13\cdot 47$ |
$3$ |
$42.8135492572$ |
$42.81354925721529$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$15.9564664432$ |
2.2.1880.1 |
$x^{2} - 470$ |
$2$ |
[2,0] |
$2^{3}\cdot 5\cdot 47$ |
$3$ |
$43.3589667774$ |
$43.3589667773576$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$8.12622244203$ |
2.2.2021.1 |
$x^{2} - x - 505$ |
$2$ |
[2,0] |
$43\cdot 47$ |
$2$ |
$44.955533586$ |
$44.955533585978046$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[3]$ |
$2$ |
$1$ |
$3.80616829641$ |
2.2.2444.1 |
$x^{2} - 611$ |
$2$ |
[2,0] |
$2^{2}\cdot 13\cdot 47$ |
$3$ |
$49.4368283772$ |
$49.4368283772331$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$13.0686503156$ |
2.0.2491.1 |
$x^{2} - x + 623$ |
$2$ |
[0,1] |
$-\,47\cdot 53$ |
$2$ |
$49.9099188539$ |
$49.90991885387112$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[12]$ |
$2$ |
0 |
$1$ |
2.0.2632.1 |
$x^{2} + 658$ |
$2$ |
[0,1] |
$-\,2^{3}\cdot 7\cdot 47$ |
$3$ |
$51.3030213535$ |
$51.30302135352264$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 4]$ |
$2$ |
0 |
$1$ |
2.0.2867.1 |
$x^{2} - x + 717$ |
$2$ |
[0,1] |
$-\,47\cdot 61$ |
$2$ |
$53.5443741209$ |
$53.54437412091022$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[12]$ |
$2$ |
0 |
$1$ |
2.0.3055.1 |
$x^{2} - x + 764$ |
$2$ |
[0,1] |
$-\,5\cdot 13\cdot 47$ |
$3$ |
$55.2720544217$ |
$55.27205442174191$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 18]$ |
$2$ |
0 |
$1$ |
2.2.3149.1 |
$x^{2} - x - 787$ |
$2$ |
[2,0] |
$47\cdot 67$ |
$2$ |
$56.1159513864$ |
$56.1159513863928$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$18.7257378303$ |
2.2.4089.1 |
$x^{2} - x - 1022$ |
$2$ |
[2,0] |
$3\cdot 29\cdot 47$ |
$3$ |
$63.945289115$ |
$63.94528911499267$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$42.3910286636$ |
2.2.4136.1 |
$x^{2} - 1034$ |
$2$ |
[2,0] |
$2^{3}\cdot 11\cdot 47$ |
$3$ |
$64.3117407633$ |
$64.31174076325411$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$10.3662777263$ |
2.0.4183.1 |
$x^{2} - x + 1046$ |
$2$ |
[0,1] |
$-\,47\cdot 89$ |
$2$ |
$64.6761161481$ |
$64.67611614808051$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[28]$ |
$2$ |
0 |
$1$ |
2.2.4277.1 |
$x^{2} - x - 1069$ |
$2$ |
[2,0] |
$7\cdot 13\cdot 47$ |
$3$ |
$65.398776747$ |
$65.39877674696982$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$5.78995081877$ |
2.0.4559.1 |
$x^{2} - x + 1140$ |
$2$ |
[0,1] |
$-\,47\cdot 97$ |
$2$ |
$67.5203672976$ |
$67.52036729757918$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[72]$ |
$2$ |
0 |
$1$ |
2.0.4747.1 |
$x^{2} - x + 1187$ |
$2$ |
[0,1] |
$-\,47\cdot 101$ |
$2$ |
$68.8984760354$ |
$68.89847603539573$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[8]$ |
$2$ |
0 |
$1$ |
2.2.4888.1 |
$x^{2} - 1222$ |
$2$ |
[2,0] |
$2^{3}\cdot 13\cdot 47$ |
$3$ |
$69.9142331718$ |
$69.91423317179414$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$30.3698262204$ |
2.2.5029.1 |
$x^{2} - x - 1257$ |
$2$ |
[2,0] |
$47\cdot 107$ |
$2$ |
$70.915442606$ |
$70.9154426059656$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$31.6684936365$ |
2.2.5452.1 |
$x^{2} - 1363$ |
$2$ |
[2,0] |
$2^{2}\cdot 29\cdot 47$ |
$3$ |
$73.8376597679$ |
$73.83765976789893$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$15.7475321343$ |
2.2.5640.1 |
$x^{2} - 1410$ |
$2$ |
[2,0] |
$2^{3}\cdot 3\cdot 5\cdot 47$ |
$4$ |
$75.0999334221$ |
$75.09993342207434$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 2]$ |
$2$ |
$1$ |
$7.31455238906$ |
2.2.5781.1 |
$x^{2} - x - 1445$ |
$2$ |
[2,0] |
$3\cdot 41\cdot 47$ |
$3$ |
$76.0328876211$ |
$76.03288762108144$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$15.6713439092$ |
2.2.5969.1 |
$x^{2} - x - 1492$ |
$2$ |
[2,0] |
$47\cdot 127$ |
$2$ |
$77.2593036469$ |
$77.25930364687478$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$59.377940725$ |
2.2.6204.1 |
$x^{2} - 1551$ |
$2$ |
[2,0] |
$2^{2}\cdot 3\cdot 11\cdot 47$ |
$4$ |
$78.7654746701$ |
$78.76547467006087$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 2]$ |
$2$ |
$1$ |
$15.1239520204$ |
2.0.6392.1 |
$x^{2} + 1598$ |
$2$ |
[0,1] |
$-\,2^{3}\cdot 17\cdot 47$ |
$3$ |
$79.9499843652$ |
$79.94998436522674$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[4, 8]$ |
$2$ |
0 |
$1$ |
2.2.6533.1 |
$x^{2} - x - 1633$ |
$2$ |
[2,0] |
$47\cdot 139$ |
$2$ |
$80.826975695$ |
$80.82697569499925$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$16.2673274816$ |
2.0.6815.1 |
$x^{2} - x + 1704$ |
$2$ |
[0,1] |
$-\,5\cdot 29\cdot 47$ |
$3$ |
$82.5530132703$ |
$82.55301327026167$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 46]$ |
$2$ |
0 |
$1$ |
2.0.7003.1 |
$x^{2} - x + 1751$ |
$2$ |
[0,1] |
$-\,47\cdot 149$ |
$2$ |
$83.6839291621$ |
$83.68392916205596$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[16]$ |
$2$ |
0 |
$1$ |
2.2.7097.1 |
$x^{2} - x - 1774$ |
$2$ |
[2,0] |
$47\cdot 151$ |
$2$ |
$84.243694126$ |
$84.2436941260294$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$47.0366427314$ |
2.2.7144.1 |
$x^{2} - 1786$ |
$2$ |
[2,0] |
$2^{3}\cdot 19\cdot 47$ |
$3$ |
$84.5221864365$ |
$84.52218643646175$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$46.4972198408$ |
2.0.7379.1 |
$x^{2} - x + 1845$ |
$2$ |
[0,1] |
$-\,47\cdot 157$ |
$2$ |
$85.90110593$ |
$85.901105930017$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[28]$ |
$2$ |
0 |
$1$ |
2.2.7661.1 |
$x^{2} - x - 1915$ |
$2$ |
[2,0] |
$47\cdot 163$ |
$2$ |
$87.5271386485$ |
$87.52713864853574$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$30.7743823338$ |
2.2.7708.1 |
$x^{2} - 1927$ |
$2$ |
[2,0] |
$2^{2}\cdot 41\cdot 47$ |
$3$ |
$87.7952162706$ |
$87.79521627059188$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$32.1665561331$ |
2.0.7755.1 |
$x^{2} - x + 1939$ |
$2$ |
[0,1] |
$-\,3\cdot 5\cdot 11\cdot 47$ |
$4$ |
$88.0624778211$ |
$88.06247782114696$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 2, 4]$ |
$2$ |
0 |
$1$ |
2.2.7849.1 |
$x^{2} - x - 1962$ |
$2$ |
[2,0] |
$47\cdot 167$ |
$2$ |
$88.5945822271$ |
$88.5945822271317$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$162.715175325$ |
2.0.7896.1 |
$x^{2} + 1974$ |
$2$ |
[0,1] |
$-\,2^{3}\cdot 3\cdot 7\cdot 47$ |
$4$ |
$88.8594395661$ |
$88.85943956609225$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 2, 8]$ |
$2$ |
0 |
$1$ |
2.0.8131.1 |
$x^{2} - x + 2033$ |
$2$ |
[0,1] |
$-\,47\cdot 173$ |
$2$ |
$90.1720577563$ |
$90.17205775626948$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[12]$ |
$2$ |
0 |
$1$ |