| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
| 3.1.175.1 |
$x^{3} - x^{2} + 2 x - 3$ |
$3$ |
[1,1] |
$-\,5^{2}\cdot 7$ |
$2$ |
$5.59344471041$ |
$7.736223764452809$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$1.28850651272$ |
| 3.1.200.1 |
$x^{3} - x^{2} + 2 x + 2$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 5^{2}$ |
$2$ |
$5.84803547643$ |
$8.270371084000274$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$2.60439940759$ |
| 3.1.300.1 |
$x^{3} - x^{2} - 3 x - 3$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3\cdot 5^{2}$ |
$3$ |
$6.69432950082$ |
$8.039467687661697$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$3.14854957566$ |
| 3.1.675.1 |
$x^{3} - 5$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 5^{2}$ |
$2$ |
$8.77205321464$ |
$10.534682878229944$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$4.81198653951$ |
| 3.1.1075.1 |
$x^{3} - x^{2} + 2 x + 12$ |
$3$ |
[1,1] |
$-\,5^{2}\cdot 43$ |
$2$ |
$10.2439980726$ |
$19.17406656229945$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$6.58332695406$ |
| 3.1.1175.1 |
$x^{3} + 5 x - 5$ |
$3$ |
[1,1] |
$-\,5^{2}\cdot 47$ |
$2$ |
$10.5522714725$ |
$20.046055658633293$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$2.03126124223$ |
| 3.1.1300.1 |
$x^{3} - x^{2} - 3 x - 13$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 5^{2}\cdot 13$ |
$3$ |
$10.9139288306$ |
$21.085391770985456$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$10.1398630277$ |
| 3.3.1300.1 |
$x^{3} - 10 x - 10$ |
$3$ |
[3,0] |
$2^{2}\cdot 5^{2}\cdot 13$ |
$3$ |
$10.9139288306$ |
$16.735486539211966$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$6.55000546582$ |
| 3.3.1425.1 |
$x^{3} - x^{2} - 8 x - 3$ |
$3$ |
[3,0] |
$3\cdot 5^{2}\cdot 19$ |
$3$ |
$11.2530855734$ |
$22.07584980930199$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$6.6762639812$ |
| 3.1.1675.1 |
$x^{3} - x^{2} + 7 x + 2$ |
$3$ |
[1,1] |
$-\,5^{2}\cdot 67$ |
$2$ |
$11.8760386903$ |
$23.934116698484896$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$8.65921215673$ |
| 3.1.1700.1 |
$x^{3} - x^{2} + 12 x - 8$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 5^{2}\cdot 17$ |
$3$ |
$11.9348319193$ |
$24.11206797166259$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$9.11636047909$ |
| 3.3.1825.1 |
$x^{3} - x^{2} - 8 x + 7$ |
$3$ |
[3,0] |
$5^{2}\cdot 73$ |
$2$ |
$12.2204619442$ |
$24.982818506665623$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$4.48807298189$ |
| 3.1.2075.1 |
$x^{3} - 10 x - 15$ |
$3$ |
[1,1] |
$-\,5^{2}\cdot 83$ |
$2$ |
$12.7547720187$ |
$26.63906938822806$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$4.85337081513$ |
| 3.1.2075.2 |
$x^{3} - x^{2} + 7 x - 8$ |
$3$ |
[1,1] |
$-\,5^{2}\cdot 83$ |
$2$ |
$12.7547720187$ |
$26.63906938822806$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$2.11104798206$ |
| 3.1.2075.3 |
$x^{3} - x^{2} - 3 x - 8$ |
$3$ |
[1,1] |
$-\,5^{2}\cdot 83$ |
$2$ |
$12.7547720187$ |
$26.63906938822806$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$2.86490226354$ |
| 3.1.2200.1 |
$x^{3} - 5 x - 10$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 5^{2}\cdot 11$ |
$3$ |
$13.0059144685$ |
$27.42971776263377$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$14.6423723013$ |
| 3.3.2300.1 |
$x^{3} - x^{2} - 8 x + 2$ |
$3$ |
[3,0] |
$2^{2}\cdot 5^{2}\cdot 23$ |
$3$ |
$13.200061218$ |
$28.046192887293646$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$18.115270693$ |
| 3.1.2575.1 |
$x^{3} - 5 x - 20$ |
$3$ |
[1,1] |
$-\,5^{2}\cdot 103$ |
$2$ |
$13.7064739325$ |
$29.675538959528588$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$24.6137459227$ |
| 3.1.2700.1 |
$x^{3} - 20$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{3}\cdot 5^{2}$ |
$3$ |
$13.9247665008$ |
$16.722766683053592$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$3.4937694211$ |
| 3.3.2700.1 |
$x^{3} - 15 x - 20$ |
$3$ |
[3,0] |
$2^{2}\cdot 3^{3}\cdot 5^{2}$ |
$3$ |
$13.9247665008$ |
$21.069365756459888$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$20.369355187$ |
| 3.1.3075.1 |
$x^{3} - x^{2} - 3 x + 12$ |
$3$ |
[1,1] |
$-\,3\cdot 5^{2}\cdot 41$ |
$3$ |
$14.541695288$ |
$32.42892547103848$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$15.1066430535$ |
| 3.1.3175.1 |
$x^{3} - x^{2} - 8 x + 17$ |
$3$ |
[1,1] |
$-\,5^{2}\cdot 127$ |
$2$ |
$14.6976502947$ |
$32.95200640537238$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$3.32840208338$ |
| 3.1.3300.1 |
$x^{3} - x^{2} + 12 x + 12$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3\cdot 5^{2}\cdot 11$ |
$4$ |
$14.8880555295$ |
$33.59440615350449$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$22.1211584656$ |
| 3.3.3325.1 |
$x^{3} - 10 x - 5$ |
$3$ |
[3,0] |
$5^{2}\cdot 7\cdot 19$ |
$3$ |
$14.9255570873$ |
$33.7214175938676$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$13.2613368258$ |
| 3.1.3575.1 |
$x^{3} - x^{2} - 8 x - 33$ |
$3$ |
[1,1] |
$-\,5^{2}\cdot 11\cdot 13$ |
$3$ |
$15.2906289177$ |
$34.966166531003054$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$11.1512809626$ |
| 3.1.3675.1 |
$x^{3} - 35$ |
$3$ |
[1,1] |
$-\,3\cdot 5^{2}\cdot 7^{2}$ |
$3$ |
$15.4318898408$ |
$18.532726798013343$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$5.62790570306$ |
| 3.1.3700.1 |
$x^{3} + 10 x - 20$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 5^{2}\cdot 37$ |
$3$ |
$15.4668037377$ |
$35.57221107185714$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$19.6504937158$ |
| 3.1.4075.1 |
$x^{3} - x^{2} - 13 x - 18$ |
$3$ |
[1,1] |
$-\,5^{2}\cdot 163$ |
$2$ |
$15.9726093864$ |
$37.331359425307674$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$14.4332459161$ |
| 3.1.4175.1 |
$x^{3} - x^{2} + 2 x - 13$ |
$3$ |
[1,1] |
$-\,5^{2}\cdot 167$ |
$2$ |
$16.1022102594$ |
$37.78663673145629$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$4.28895741568$ |
| 3.1.4200.1 |
$x^{3} - x^{2} + 2 x - 38$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3\cdot 5^{2}\cdot 7$ |
$4$ |
$16.1342864602$ |
$37.899601517805245$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$27.5717118534$ |
| 3.1.4300.1 |
$x^{3} - x^{2} + 7 x - 13$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 5^{2}\cdot 43$ |
$3$ |
$16.2613333168$ |
$30.436933431502425$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$4.53456050196$ |
| 3.1.4300.2 |
$x^{3} - x^{2} - 13 x + 27$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 5^{2}\cdot 43$ |
$3$ |
$16.2613333168$ |
$30.436933431502425$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$3.75410689948$ |
| 3.1.4575.1 |
$x^{3} - 15 x - 45$ |
$3$ |
[1,1] |
$-\,3\cdot 5^{2}\cdot 61$ |
$3$ |
$16.6008515555$ |
$39.55537878985837$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$8.99998754068$ |
| 3.1.4675.1 |
$x^{3} + 10 x - 5$ |
$3$ |
[1,1] |
$-\,5^{2}\cdot 11\cdot 17$ |
$3$ |
$16.7209342213$ |
$39.985341190775294$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[4]$ |
$[4]$ |
$2$ |
$1$ |
$3.75958631323$ |
| 3.3.4825.1 |
$x^{3} - x^{2} - 18 x - 8$ |
$3$ |
[3,0] |
$5^{2}\cdot 193$ |
$2$ |
$16.8978884656$ |
$40.621752652279945$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$36.3964999556$ |
| 3.1.5075.1 |
$x^{3} - x^{2} + 2 x - 28$ |
$3$ |
[1,1] |
$-\,5^{2}\cdot 7\cdot 29$ |
$3$ |
$17.1848342973$ |
$41.66083995644888$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$11.8825768857$ |
| 3.3.5300.1 |
$x^{3} - 20 x - 20$ |
$3$ |
[3,0] |
$2^{2}\cdot 5^{2}\cdot 53$ |
$3$ |
$17.4351340127$ |
$33.791276769558415$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$17.8886013912$ |
| 3.3.5325.1 |
$x^{3} - x^{2} - 13 x - 8$ |
$3$ |
[3,0] |
$3\cdot 5^{2}\cdot 71$ |
$3$ |
$17.4625047546$ |
$42.67463395520438$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$27.4729572815$ |
| 3.1.5575.1 |
$x^{3} - 5 x - 15$ |
$3$ |
[1,1] |
$-\,5^{2}\cdot 223$ |
$2$ |
$17.7316148987$ |
$43.6648964334569$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$7.94732215118$ |
| 3.1.5675.1 |
$x^{3} - x^{2} + 12 x + 52$ |
$3$ |
[1,1] |
$-\,5^{2}\cdot 227$ |
$2$ |
$17.8370058721$ |
$44.054769315910065$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$4.96367527283$ |
| 3.1.5700.1 |
$x^{3} - x^{2} + 17 x + 7$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3\cdot 5^{2}\cdot 19$ |
$4$ |
$17.8631598771$ |
$44.15169961860398$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$31.1708053547$ |
| 3.1.5800.1 |
$x^{3} - x^{2} - 8 x - 28$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 5^{2}\cdot 29$ |
$3$ |
$17.9670177914$ |
$44.53731130350112$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$25.5174971396$ |
| 3.3.5925.1 |
$x^{3} - x^{2} - 18 x + 12$ |
$3$ |
[3,0] |
$3\cdot 5^{2}\cdot 79$ |
$3$ |
$18.0951748888$ |
$45.0146809031441$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$29.500625439$ |
| 3.1.6075.1 |
$x^{3} - 45$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 5^{2}$ |
$2$ |
$18.2466059867$ |
$21.91302343598798$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$15.3044343837$ |
| 3.1.6075.2 |
$x^{3} - 15$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 5^{2}$ |
$2$ |
$18.2466059867$ |
$21.91302343598798$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$9.69295167783$ |
| 3.1.6200.1 |
$x^{3} + 5 x - 30$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 5^{2}\cdot 31$ |
$3$ |
$18.3709055001$ |
$46.04747738887663$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$39.5435526726$ |
| 3.1.6575.1 |
$x^{3} + 5 x - 15$ |
$3$ |
[1,1] |
$-\,5^{2}\cdot 263$ |
$2$ |
$18.7340605277$ |
$47.419599005894774$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$16.8808389943$ |
| 3.1.6675.1 |
$x^{3} - x^{2} + 7 x + 12$ |
$3$ |
[1,1] |
$-\,3\cdot 5^{2}\cdot 89$ |
$3$ |
$18.8285592793$ |
$47.77884352737507$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$24.0659240733$ |
| 3.1.6700.1 |
$x^{3} - x^{2} - 3 x + 17$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 5^{2}\cdot 67$ |
$3$ |
$18.8520363102$ |
$37.99304202510457$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$5.20909790287$ |
| 3.1.6700.2 |
$x^{3} + 10 x - 10$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 5^{2}\cdot 67$ |
$3$ |
$18.8520363102$ |
$37.99304202510457$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$[6]$ |
$2$ |
$1$ |
$2.54719483066$ |
