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 |
2.2.76.1 |
$x^{2} - 19$ |
$2$ |
[2,0] |
$2^{2}\cdot 19$ |
$2$ |
$8.71779788708$ |
$8.717797887081348$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$5.82893696698$ |
2.2.133.1 |
$x^{2} - x - 33$ |
$2$ |
[2,0] |
$7\cdot 19$ |
$2$ |
$11.5325625947$ |
$11.532562594670797$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$5.15325818041$ |
2.0.152.1 |
$x^{2} + 38$ |
$2$ |
[0,1] |
$-\,2^{3}\cdot 19$ |
$2$ |
$12.3288280059$ |
$12.328828005937952$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[6]$ |
$2$ |
0 |
$1$ |
2.2.209.1 |
$x^{2} - x - 52$ |
$2$ |
[2,0] |
$11\cdot 19$ |
$2$ |
$14.4568322948$ |
$14.45683229480096$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$11.4414509452$ |
2.0.228.1 |
$x^{2} + 57$ |
$2$ |
[0,1] |
$-\,2^{2}\cdot 3\cdot 19$ |
$3$ |
$15.0996688705$ |
$15.0996688705415$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 2]$ |
$2$ |
0 |
$1$ |
2.0.247.1 |
$x^{2} - x + 62$ |
$2$ |
[0,1] |
$-\,13\cdot 19$ |
$2$ |
$15.7162336455$ |
$15.716233645501712$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[6]$ |
$2$ |
0 |
$1$ |
2.2.380.1 |
$x^{2} - 95$ |
$2$ |
[2,0] |
$2^{2}\cdot 5\cdot 19$ |
$3$ |
$19.4935886896$ |
$19.493588689617926$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$4.3565444206$ |
2.0.399.1 |
$x^{2} - x + 100$ |
$2$ |
[0,1] |
$-\,3\cdot 7\cdot 19$ |
$3$ |
$19.9749843554$ |
$19.974984355438178$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 8]$ |
$2$ |
0 |
$1$ |
2.2.437.1 |
$x^{2} - x - 109$ |
$2$ |
[2,0] |
$19\cdot 23$ |
$2$ |
$20.9045449604$ |
$20.904544960366874$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$3.04224711209$ |
2.2.456.1 |
$x^{2} - 114$ |
$2$ |
[2,0] |
$2^{3}\cdot 3\cdot 19$ |
$3$ |
$21.3541565041$ |
$21.354156504062622$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$7.62559483418$ |
2.0.551.1 |
$x^{2} - x + 138$ |
$2$ |
[0,1] |
$-\,19\cdot 29$ |
$2$ |
$23.4733891886$ |
$23.473389188611005$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[26]$ |
$2$ |
0 |
$1$ |
2.0.627.1 |
$x^{2} - x + 157$ |
$2$ |
[0,1] |
$-\,3\cdot 11\cdot 19$ |
$3$ |
$25.0399680511$ |
$25.03996805109783$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 2]$ |
$2$ |
0 |
$1$ |
2.2.665.1 |
$x^{2} - x - 166$ |
$2$ |
[2,0] |
$5\cdot 7\cdot 19$ |
$3$ |
$25.7875939165$ |
$25.787593916455254$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$10.2196841916$ |
2.0.703.1 |
$x^{2} - x + 176$ |
$2$ |
[0,1] |
$-\,19\cdot 37$ |
$2$ |
$26.5141471671$ |
$26.514147167125703$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[14]$ |
$2$ |
0 |
$1$ |
2.2.741.1 |
$x^{2} - x - 185$ |
$2$ |
[2,0] |
$3\cdot 13\cdot 19$ |
$3$ |
$27.2213151776$ |
$27.2213151776324$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$5.5012415504$ |
2.0.760.1 |
$x^{2} + 190$ |
$2$ |
[0,1] |
$-\,2^{3}\cdot 5\cdot 19$ |
$3$ |
$27.5680975042$ |
$27.568097504180443$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 2]$ |
$2$ |
0 |
$1$ |
2.0.779.1 |
$x^{2} - x + 195$ |
$2$ |
[0,1] |
$-\,19\cdot 41$ |
$2$ |
$27.9105714739$ |
$27.910571473905726$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[10]$ |
$2$ |
0 |
$1$ |
2.2.817.1 |
$x^{2} - x - 204$ |
$2$ |
[2,0] |
$19\cdot 43$ |
$2$ |
$28.5832118559$ |
$28.583211855912904$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[5]$ |
$2$ |
$1$ |
$6.53087550275$ |
2.2.893.1 |
$x^{2} - x - 223$ |
$2$ |
[2,0] |
$19\cdot 47$ |
$2$ |
$29.883105595$ |
$29.88310559496787$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$7.74109890116$ |
2.0.1007.1 |
$x^{2} - x + 252$ |
$2$ |
[0,1] |
$-\,19\cdot 53$ |
$2$ |
$31.7332633052$ |
$31.73326330524486$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[30]$ |
$2$ |
0 |
$1$ |
2.2.1045.1 |
$x^{2} - x - 261$ |
$2$ |
[2,0] |
$5\cdot 11\cdot 19$ |
$3$ |
$32.3264597505$ |
$32.32645975048923$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[4]$ |
$2$ |
$1$ |
$4.57460468034$ |
2.0.1064.1 |
$x^{2} + 266$ |
$2$ |
[0,1] |
$-\,2^{3}\cdot 7\cdot 19$ |
$3$ |
$32.6190128606$ |
$32.61901286060018$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 10]$ |
$2$ |
0 |
$1$ |
2.0.1140.1 |
$x^{2} + 285$ |
$2$ |
[0,1] |
$-\,2^{2}\cdot 3\cdot 5\cdot 19$ |
$4$ |
$33.7638860323$ |
$33.76388603226827$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 2, 4]$ |
$2$ |
0 |
$1$ |
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 |
$1$ |
2.2.1292.1 |
$x^{2} - 323$ |
$2$ |
[2,0] |
$2^{2}\cdot 17\cdot 19$ |
$3$ |
$35.9444015112$ |
$35.94440151122286$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[4]$ |
$2$ |
$1$ |
$3.58274643892$ |
2.0.1311.1 |
$x^{2} - x + 328$ |
$2$ |
[0,1] |
$-\,3\cdot 19\cdot 23$ |
$3$ |
$36.2077339805$ |
$36.207733980463345$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 14]$ |
$2$ |
0 |
$1$ |
2.2.1577.1 |
$x^{2} - x - 394$ |
$2$ |
[2,0] |
$19\cdot 83$ |
$2$ |
$39.7114593033$ |
$39.71145930332956$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$33.0455807758$ |
2.2.1653.1 |
$x^{2} - x - 413$ |
$2$ |
[2,0] |
$3\cdot 19\cdot 29$ |
$3$ |
$40.6571027005$ |
$40.65710270051225$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$7.26052210425$ |
2.0.1672.1 |
$x^{2} + 418$ |
$2$ |
[0,1] |
$-\,2^{3}\cdot 11\cdot 19$ |
$3$ |
$40.8900966005$ |
$40.890096600521744$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 4]$ |
$2$ |
0 |
$1$ |
2.0.1691.1 |
$x^{2} - x + 423$ |
$2$ |
[0,1] |
$-\,19\cdot 89$ |
$2$ |
$41.1217703899$ |
$41.12177038990418$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[18]$ |
$2$ |
0 |
$1$ |
2.0.1843.1 |
$x^{2} - x + 461$ |
$2$ |
[0,1] |
$-\,19\cdot 97$ |
$2$ |
$42.9301758673$ |
$42.930175867331364$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[6]$ |
$2$ |
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) |
$[2]$ |
$2$ |
$1$ |
$11.8918412378$ |
2.0.1995.1 |
$x^{2} - x + 499$ |
$2$ |
[0,1] |
$-\,3\cdot 5\cdot 7\cdot 19$ |
$4$ |
$44.6654228683$ |
$44.66542286825459$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 2, 2]$ |
$2$ |
0 |
$1$ |
2.0.2071.1 |
$x^{2} - x + 518$ |
$2$ |
[0,1] |
$-\,19\cdot 109$ |
$2$ |
$45.5082410119$ |
$45.50824101193101$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[30]$ |
$2$ |
0 |
$1$ |
2.2.2109.1 |
$x^{2} - x - 527$ |
$2$ |
[2,0] |
$3\cdot 19\cdot 37$ |
$3$ |
$45.9238500128$ |
$45.92385001282014$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$11.6852387725$ |
2.0.2147.1 |
$x^{2} - x + 537$ |
$2$ |
[0,1] |
$-\,19\cdot 113$ |
$2$ |
$46.3357313528$ |
$46.33573135281238$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[14]$ |
$2$ |
0 |
$1$ |
2.2.2185.1 |
$x^{2} - x - 546$ |
$2$ |
[2,0] |
$5\cdot 19\cdot 23$ |
$3$ |
$46.7439835701$ |
$46.74398357008097$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$36.1488109197$ |
2.2.2261.1 |
$x^{2} - x - 565$ |
$2$ |
[2,0] |
$7\cdot 17\cdot 19$ |
$3$ |
$47.5499737119$ |
$47.54997371187496$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$7.55066096668$ |
2.2.2280.1 |
$x^{2} - 570$ |
$2$ |
[2,0] |
$2^{3}\cdot 3\cdot 5\cdot 19$ |
$4$ |
$47.7493455453$ |
$47.74934554525329$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 2]$ |
$2$ |
$1$ |
$5.94541375565$ |
2.2.2337.1 |
$x^{2} - x - 584$ |
$2$ |
[2,0] |
$3\cdot 19\cdot 41$ |
$3$ |
$48.3425278611$ |
$48.342527861087284$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$21.0198154855$ |
2.0.2356.1 |
$x^{2} + 589$ |
$2$ |
[0,1] |
$-\,2^{2}\cdot 19\cdot 31$ |
$3$ |
$48.538644398$ |
$48.53864439804639$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 8]$ |
$2$ |
0 |
$1$ |
2.0.2451.1 |
$x^{2} - x + 613$ |
$2$ |
[0,1] |
$-\,3\cdot 19\cdot 43$ |
$3$ |
$49.5075751779$ |
$49.50757517794625$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 4]$ |
$2$ |
0 |
$1$ |
2.2.2489.1 |
$x^{2} - x - 622$ |
$2$ |
[2,0] |
$19\cdot 131$ |
$2$ |
$49.8898787331$ |
$49.889878733065686$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$51.395314785$ |
2.0.2584.1 |
$x^{2} + 646$ |
$2$ |
[0,1] |
$-\,2^{3}\cdot 17\cdot 19$ |
$3$ |
$50.8330601086$ |
$50.83306010855534$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 8]$ |
$2$ |
0 |
$1$ |
2.2.2641.1 |
$x^{2} - x - 660$ |
$2$ |
[2,0] |
$19\cdot 139$ |
$2$ |
$51.3906606301$ |
$51.39066063011839$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$90.1229885158$ |
2.0.2679.1 |
$x^{2} - x + 670$ |
$2$ |
[0,1] |
$-\,3\cdot 19\cdot 47$ |
$3$ |
$51.7590571784$ |
$51.75905717843013$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 26]$ |
$2$ |
0 |
$1$ |
2.0.2755.1 |
$x^{2} - x + 689$ |
$2$ |
[0,1] |
$-\,5\cdot 19\cdot 29$ |
$3$ |
$52.488093888$ |
$52.48809388804284$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 4]$ |
$2$ |
0 |
$1$ |
2.2.3021.1 |
$x^{2} - x - 755$ |
$2$ |
[2,0] |
$3\cdot 19\cdot 53$ |
$3$ |
$54.9636243346$ |
$54.96362433464518$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[6]$ |
$2$ |
$1$ |
$4.00700244268$ |
2.2.3097.1 |
$x^{2} - x - 774$ |
$2$ |
[2,0] |
$19\cdot 163$ |
$2$ |
$55.6506963119$ |
$55.65069631190611$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$60.8741007532$ |
2.0.3135.1 |
$x^{2} - x + 784$ |
$2$ |
[0,1] |
$-\,3\cdot 5\cdot 11\cdot 19$ |
$4$ |
$55.9910707167$ |
$55.991070716677676$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2, 2, 10]$ |
$2$ |
0 |
$1$ |