| 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 |
Unit signature rank |
Max $p$ |
| 3.1.172.1 |
$x^{3} - x^{2} - x + 3$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 43$ |
$2$ |
$5.56129776652$ |
$10.409284811693793$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$1.88195290962$ |
$1$ |
$43$ |
| 3.3.473.1 |
$x^{3} - 5 x - 1$ |
$3$ |
(3, 0) |
$11\cdot 43$ |
$2$ |
$7.79148753564$ |
$21.748563170931547$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$2.84322939957$ |
$3$ |
$43$ |
| 3.1.516.1 |
$x^{3} - x^{2} + x - 9$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 43$ |
$3$ |
$8.02077931412$ |
$22.715633383201094$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$6.38507778986$ |
$1$ |
$43$ |
| 3.1.731.1 |
$x^{3} - x^{2} + 3 x + 4$ |
$3$ |
(1, 1) |
$-\,17\cdot 43$ |
$2$ |
$9.00822293742$ |
$27.03701166919155$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$2.01267869245$ |
$1$ |
$43$ |
| 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 |
$2$ |
$1$ |
$6.58332695406$ |
$1$ |
$43$ |
| 3.1.1419.1 |
$x^{3} - x^{2} + 10 x - 12$ |
$3$ |
(1, 1) |
$-\,3\cdot 11\cdot 43$ |
$3$ |
$11.2372695503$ |
$37.66961640367472$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$8.61938596484$ |
$1$ |
$43$ |
| 3.1.1720.1 |
$x^{3} - 2 x - 16$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 5\cdot 43$ |
$3$ |
$11.9814528298$ |
$41.47288270665544$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$13.0675755571$ |
$1$ |
$43$ |
| 3.1.1763.1 |
$x^{3} + 11 x - 8$ |
$3$ |
(1, 1) |
$-\,41\cdot 43$ |
$2$ |
$12.0804775917$ |
$41.98809355043403$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$6.01867017906$ |
$1$ |
$43$ |
| 3.1.1892.1 |
$x^{3} - x^{2} + x - 17$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 11\cdot 43$ |
$3$ |
$12.3682155105$ |
$43.497126341863094$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$10.1412831342$ |
$1$ |
$43$ |
| 3.3.2021.1 |
$x^{3} - 8 x - 1$ |
$3$ |
(3, 0) |
$43\cdot 47$ |
$2$ |
$12.6431542894$ |
$44.955533585978046$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$11.5183824927$ |
$2$ |
$47$ |
| 3.1.2408.1 |
$x^{3} - x^{2} + 2 x - 10$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 7\cdot 43$ |
$3$ |
$13.4035187908$ |
$49.07137658554119$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$12.1110859192$ |
$1$ |
$43$ |
| 3.1.2795.1 |
$x^{3} - x^{2} + 10 x - 20$ |
$3$ |
(1, 1) |
$-\,5\cdot 13\cdot 43$ |
$3$ |
$14.086202824$ |
$52.86775955154521$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$9.64588296043$ |
$1$ |
$43$ |
| 3.1.3268.1 |
$x^{3} + x - 22$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 19\cdot 43$ |
$3$ |
$14.8397761292$ |
$57.16642371182581$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$17.2586511294$ |
$1$ |
$43$ |
| 3.1.3311.1 |
$x^{3} - x^{2} - 11$ |
$3$ |
(1, 1) |
$-\,7\cdot 11\cdot 43$ |
$3$ |
$14.9045794671$ |
$57.54128952326321$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$4.33090870198$ |
$1$ |
$43$ |
| 3.1.3483.1 |
$x^{3} + 15 x - 4$ |
$3$ |
(1, 1) |
$-\,3^{4}\cdot 43$ |
$2$ |
$15.1583230416$ |
$28.37238868197542$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$12.1861709357$ |
$1$ |
$43$ |
| 3.3.3569.1 |
$x^{3} - x^{2} - 10 x + 9$ |
$3$ |
(3, 0) |
$43\cdot 83$ |
$2$ |
$15.2820699296$ |
$59.74110812497538$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$7.79371883094$ |
$3$ |
$83$ |
| 3.1.3956.1 |
$x^{3} - x^{2} - 4 x + 14$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 23\cdot 43$ |
$3$ |
$15.8155910833$ |
$62.89674077406555$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$18.2466870659$ |
$1$ |
$43$ |
| 3.1.3999.1 |
$x^{3} + 9 x - 35$ |
$3$ |
(1, 1) |
$-\,3\cdot 31\cdot 43$ |
$3$ |
$15.8726875752$ |
$63.23764701504951$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$11.3258124383$ |
$1$ |
$43$ |
| 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) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$4.53456050196$ |
$1$ |
$43$ |
| 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) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$3.75410689948$ |
$1$ |
$43$ |
| 3.1.4472.1 |
$x^{3} + 14 x - 16$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 13\cdot 43$ |
$3$ |
$16.4753227686$ |
$66.87301398920195$ |
|
|
|
$S_3$ (as 3T2) |
$[5]$ |
$[5]$ |
$2$ |
$1$ |
$2.84363127265$ |
$1$ |
$43$ |
| 3.1.4859.1 |
$x^{3} - x^{2} + 11 x - 4$ |
$3$ |
(1, 1) |
$-\,43\cdot 113$ |
$2$ |
$16.9374866673$ |
$69.70652767137379$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$9.88124261793$ |
$1$ |
$113$ |
| 3.1.6063.1 |
$x^{3} - 3 x - 45$ |
$3$ |
(1, 1) |
$-\,3\cdot 43\cdot 47$ |
$3$ |
$18.2345838413$ |
$77.86526825228306$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$10.2971839501$ |
$1$ |
$47$ |
| 3.1.6235.1 |
$x^{3} - x^{2} - x + 46$ |
$3$ |
(1, 1) |
$-\,5\cdot 29\cdot 43$ |
$3$ |
$18.4054095626$ |
$78.96201618499872$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$18.8763586102$ |
$1$ |
$43$ |
| 3.1.6751.1 |
$x^{3} - x^{2} - 22 x + 51$ |
$3$ |
(1, 1) |
$-\,43\cdot 157$ |
$2$ |
$18.8997489772$ |
$82.16446920658588$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$7.62707449932$ |
$1$ |
$157$ |
| 3.1.7052.1 |
$x^{3} - x^{2} + 7 x - 17$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 41\cdot 43$ |
$3$ |
$19.1765628374$ |
$66.65194387209816$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$2.68537313887$ |
$1$ |
$43$ |
| 3.1.7052.2 |
$x^{3} - x^{2} + 3 x - 17$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 41\cdot 43$ |
$3$ |
$19.1765628374$ |
$66.65194387209816$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$4.20757937446$ |
$1$ |
$43$ |
| 3.1.7052.3 |
$x^{3} - x^{2} + 11 x + 43$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 41\cdot 43$ |
$3$ |
$19.1765628374$ |
$66.65194387209816$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$8.5827972619$ |
$1$ |
$43$ |
| 3.3.7224.1 |
$x^{3} - x^{2} - 19 x + 7$ |
$3$ |
(3, 0) |
$2^{3}\cdot 3\cdot 7\cdot 43$ |
$4$ |
$19.3312192166$ |
$84.99411744350311$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$44.9440267997$ |
$3$ |
$43$ |
| 3.1.7267.1 |
$x^{3} - x^{2} - 17 x + 38$ |
$3$ |
(1, 1) |
$-\,13^{2}\cdot 43$ |
$2$ |
$19.3694989586$ |
$36.25460095540845$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$6.19423876071$ |
$1$ |
$43$ |
| 3.1.7912.1 |
$x^{3} + 10 x - 32$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 23\cdot 43$ |
$3$ |
$19.9263961224$ |
$88.94942383174835$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$15.1215057827$ |
$1$ |
$43$ |
| 3.1.8127.1 |
$x^{3} + 15 x - 47$ |
$3$ |
(1, 1) |
$-\,3^{3}\cdot 7\cdot 43$ |
$3$ |
$20.1052781861$ |
$62.50643235670045$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$5.70341564325$ |
$1$ |
$43$ |
| 3.1.8772.1 |
$x^{3} - x^{2} - 54$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 17\cdot 43$ |
$4$ |
$20.6236821931$ |
$93.65895579174476$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$40.2193672568$ |
$1$ |
$43$ |
| 3.1.8815.1 |
$x^{3} + 13 x - 1$ |
$3$ |
(1, 1) |
$-\,5\cdot 41\cdot 43$ |
$3$ |
$20.6573261063$ |
$93.888231424391$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[5]$ |
$[5]$ |
$2$ |
$1$ |
$2.56540400654$ |
$1$ |
$43$ |
| 3.3.9073.1 |
$x^{3} - x^{2} - 16 x + 23$ |
$3$ |
(3, 0) |
$43\cdot 211$ |
$2$ |
$20.856926161$ |
$95.25229656024048$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$11.4682410223$ |
$3$ |
$211$ |
| 3.1.9159.1 |
$x^{3} + 21 x - 41$ |
$3$ |
(1, 1) |
$-\,3\cdot 43\cdot 71$ |
$3$ |
$20.9226177007$ |
$95.7026645397086$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$12.9203524581$ |
$1$ |
$71$ |
| 3.1.9288.1 |
$x^{3} + 21 x - 2$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 3^{3}\cdot 43$ |
$3$ |
$21.0203883623$ |
$66.82218695666684$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$29.0562039878$ |
$1$ |
$43$ |
| 3.3.9460.1 |
$x^{3} - x^{2} - 21 x + 1$ |
$3$ |
(3, 0) |
$2^{2}\cdot 5\cdot 11\cdot 43$ |
$4$ |
$21.1493510262$ |
$77.19732227223137$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$20.8421085391$ |
$3$ |
$43$ |
| 3.1.9804.1 |
$x^{3} - x^{2} + 3 x - 39$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 19\cdot 43$ |
$4$ |
$21.4026607458$ |
$78.5883769178666$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$20.875278839$ |
$1$ |
$43$ |
| 3.1.10019.1 |
$x^{3} - x^{2} - 10 x + 44$ |
$3$ |
(1, 1) |
$-\,43\cdot 233$ |
$2$ |
$21.5579830208$ |
$100.09495491781792$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$13.8388285696$ |
$1$ |
$233$ |
| 3.1.10148.1 |
$x^{3} - x^{2} + 17 x + 23$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 43\cdot 59$ |
$3$ |
$21.6501122727$ |
$100.73728207570423$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$19.0120443872$ |
$1$ |
$59$ |
| 3.1.10191.1 |
$x^{3} + 21 x - 45$ |
$3$ |
(1, 1) |
$-\,3\cdot 43\cdot 79$ |
$3$ |
$21.6806484376$ |
$100.9504829111778$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$17.2060048318$ |
$1$ |
$79$ |
| 3.1.10535.1 |
$x^{3} - 7 x - 21$ |
$3$ |
(1, 1) |
$-\,5\cdot 7^{2}\cdot 43$ |
$3$ |
$21.9218993772$ |
$53.655954283494445$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$7.70073080025$ |
$1$ |
$43$ |
| 3.3.10664.1 |
$x^{3} - 26 x - 32$ |
$3$ |
(3, 0) |
$2^{3}\cdot 31\cdot 43$ |
$3$ |
$22.011013769$ |
$103.26664514740469$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$42.0176142126$ |
$2$ |
$43$ |
| 3.1.10707.1 |
$x^{3} - x^{2} + x - 60$ |
$3$ |
(1, 1) |
$-\,3\cdot 43\cdot 83$ |
$3$ |
$22.0405587894$ |
$103.47463457292324$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$31.0654137061$ |
$1$ |
$83$ |
| 3.3.11137.1 |
$x^{3} - x^{2} - 22 x + 8$ |
$3$ |
(3, 0) |
$7\cdot 37\cdot 43$ |
$3$ |
$22.3317491018$ |
$105.53198567259123$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$63.8365821014$ |
$3$ |
$43$ |
| 3.1.11567.1 |
$x^{3} - x^{2} - 22 x + 53$ |
$3$ |
(1, 1) |
$-\,43\cdot 269$ |
$2$ |
$22.6155373878$ |
$107.54998837749821$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$5.84962365083$ |
$1$ |
$269$ |
| 3.1.11911.1 |
$x^{3} + x - 21$ |
$3$ |
(1, 1) |
$-\,43\cdot 277$ |
$2$ |
$22.8375445847$ |
$109.13752791776072$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$9.39549261611$ |
$1$ |
$277$ |
| 3.1.12083.1 |
$x^{3} - 22 x - 45$ |
$3$ |
(1, 1) |
$-\,43\cdot 281$ |
$2$ |
$22.9469476656$ |
$109.92270011239717$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[4]$ |
$[4]$ |
$2$ |
$1$ |
$11.0478696784$ |
$1$ |
$281$ |
| 3.1.12556.1 |
$x^{3} - 8 x - 44$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 43\cdot 73$ |
$3$ |
$23.2425497384$ |
$88.93696841718867$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$14.6093493212$ |
$1$ |
$73$ |
