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 |
3.1.108.1 |
$x^{3} - 2$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{3}$ |
$2$ |
$4.7622031559$ |
$5.71910575798162$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$1.34737734833$ |
3.1.351.1 |
$x^{3} + 3 x - 3$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 13$ |
$2$ |
$7.05400406316$ |
$12.99011931146003$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$1.70227535834$ |
3.3.621.1 |
$x^{3} - 6 x - 3$ |
$3$ |
[3,0] |
$3^{3}\cdot 23$ |
$2$ |
$8.53160093955$ |
$17.278473921432806$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$5.39970280308$ |
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 |
$2$ |
$1$ |
$4.81198653951$ |
3.1.756.1 |
$x^{3} - 6 x - 12$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{3}\cdot 7$ |
$3$ |
$9.10976691563$ |
$19.06428314197696$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$7.10745968178$ |
3.1.999.1 |
$x^{3} + 3 x - 12$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 37$ |
$2$ |
$9.99666555494$ |
$21.915042936585067$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$12.5105786612$ |
3.1.1080.1 |
$x^{3} + 3 x - 6$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{3}\cdot 5$ |
$3$ |
$10.2598556801$ |
$22.786176627742247$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$9.88964144405$ |
3.1.1323.1 |
$x^{3} - 7$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 7^{2}$ |
$2$ |
$10.9779171301$ |
$13.183786372359444$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$2.44105647039$ |
3.3.1593.1 |
$x^{3} - 9 x - 7$ |
$3$ |
[3,0] |
$3^{3}\cdot 59$ |
$2$ |
$11.6789892476$ |
$27.67371536012528$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$6.33079430444$ |
3.1.1647.1 |
$x^{3} - 9 x - 13$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 61$ |
$2$ |
$11.8094915493$ |
$28.1388523948431$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$4.04672973703$ |
3.1.1971.1 |
$x^{3} - 9 x - 20$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 73$ |
$2$ |
$12.5380175891$ |
$30.782429528741996$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$11.1179700318$ |
3.1.2052.1 |
$x^{3} + 9 x - 14$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{3}\cdot 19$ |
$3$ |
$12.7074707528$ |
$31.40857695105379$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$13.4384681735$ |
3.3.2241.1 |
$x^{3} - 9 x - 5$ |
$3$ |
[3,0] |
$3^{3}\cdot 83$ |
$2$ |
$13.0862120144$ |
$32.8231690886123$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$8.26350659971$ |
3.1.2376.1 |
$x^{3} - 9 x - 14$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{3}\cdot 11$ |
$3$ |
$13.3438805434$ |
$33.79736172667132$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$14.9005947529$ |
3.1.2619.1 |
$x^{3} + 6 x - 29$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 97$ |
$2$ |
$13.7841026766$ |
$35.4835719013513$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$2$ |
$1$ |
$4.70831127318$ |
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) |
$[3]$ |
$2$ |
$1$ |
$3.4937694211$ |
3.3.2808.1 |
$x^{3} - 9 x - 2$ |
$3$ |
[3,0] |
$2^{3}\cdot 3^{3}\cdot 13$ |
$3$ |
$14.1080081263$ |
$36.74160581422285$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$20.3128560863$ |
3.3.3132.1 |
$x^{3} - 15 x - 6$ |
$3$ |
[3,0] |
$2^{2}\cdot 3^{3}\cdot 29$ |
$3$ |
$14.6309968832$ |
$38.803460559606464$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$22.4935279395$ |
3.1.3267.1 |
$x^{3} - 11$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 11^{2}$ |
$2$ |
$14.8382623297$ |
$17.819817582388065$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$2$ |
$1$ |
$5.58720662606$ |
3.1.3348.1 |
$x^{3} + 9 x - 4$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{3}\cdot 31$ |
$3$ |
$14.9598928567$ |
$40.11920388620726$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$17.9057446337$ |
3.1.3591.1 |
$x^{3} + 9 x - 5$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 7\cdot 19$ |
$3$ |
$15.313406166$ |
$41.54964182346182$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$8.81150078554$ |
3.1.3672.1 |
$x^{3} - 6 x - 24$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{3}\cdot 17$ |
$3$ |
$15.4276895439$ |
$42.01563368623955$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$19.0499832586$ |
3.1.3915.1 |
$x^{3} + 3 x - 24$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 5\cdot 29$ |
$3$ |
$15.7607636175$ |
$43.38358778675604$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$14.8192328782$ |
3.3.4104.1 |
$x^{3} - 18 x - 16$ |
$3$ |
[3,0] |
$2^{3}\cdot 3^{3}\cdot 19$ |
$3$ |
$16.0104098923$ |
$44.41843549901926$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$23.7615582112$ |
3.1.4239.1 |
$x^{3} + 9 x - 7$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 157$ |
$2$ |
$16.1840721363$ |
$45.14309075422692$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$5.0698524306$ |
3.1.4563.1 |
$x^{3} - 13$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 13^{2}$ |
$2$ |
$16.586324441$ |
$19.919129971779828$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$5.6420579792$ |
3.1.4968.1 |
$x^{3} + 15 x - 34$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{3}\cdot 23$ |
$3$ |
$17.0632018791$ |
$48.870904313600214$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$20.5711263099$ |
3.1.5211.1 |
$x^{3} - 6 x - 15$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 193$ |
$2$ |
$17.3369896955$ |
$50.05184815392902$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$19.937704382$ |
3.1.5292.1 |
$x^{3} - 14$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{3}\cdot 7^{2}$ |
$3$ |
$17.4263572007$ |
$20.927956356407396$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$4.46551305026$ |
3.1.5535.1 |
$x^{3} - 3 x - 43$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 5\cdot 41$ |
$3$ |
$17.6891056199$ |
$51.58440129745782$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$6.85433781231$ |
3.3.5724.1 |
$x^{3} - 18 x - 4$ |
$3$ |
[3,0] |
$2^{2}\cdot 3^{3}\cdot 53$ |
$3$ |
$17.8881958732$ |
$52.457718022675515$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$29.5526169061$ |
3.1.5859.1 |
$x^{3} - 12 x - 47$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 7\cdot 31$ |
$3$ |
$18.0277350208$ |
$53.07271814040024$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$14.4841411481$ |
3.1.5940.1 |
$x^{3} + 18 x - 4$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{3}\cdot 5\cdot 11$ |
$4$ |
$18.1104322104$ |
$53.43832098044126$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$28.0570112475$ |
3.1.6183.1 |
$x^{3} - 9 x - 32$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 229$ |
$2$ |
$18.3540995179$ |
$54.52042153545375$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$14.3600643393$ |
3.1.6183.2 |
$x^{3} + 3 x - 15$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 229$ |
$2$ |
$18.3540995179$ |
$54.52042153545375$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$2.73397668934$ |
3.1.6183.3 |
$x^{3} + 9 x - 11$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 229$ |
$2$ |
$18.3540995179$ |
$54.52042153545375$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$2.5056507953$ |
3.3.6453.1 |
$x^{3} - 18 x - 25$ |
$3$ |
[3,0] |
$3^{3}\cdot 239$ |
$2$ |
$18.6174653847$ |
$55.6981043279862$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$24.5262356078$ |
3.1.6507.1 |
$x^{3} + 24 x - 11$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 241$ |
$2$ |
$18.6692527596$ |
$55.93066527404058$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$2$ |
$1$ |
$9.3828647449$ |
3.1.7155.1 |
$x^{3} + 12 x - 3$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 5\cdot 53$ |
$3$ |
$19.2694748657$ |
$58.64951172160915$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[4]$ |
$2$ |
$1$ |
$5.27292078867$ |
3.3.7425.1 |
$x^{3} - 15 x - 15$ |
$3$ |
[3,0] |
$3^{3}\cdot 5^{2}\cdot 11$ |
$3$ |
$19.5088717028$ |
$34.93959039247001$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$13.3990738676$ |
3.1.7479.1 |
$x^{3} + 9 x - 13$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 277$ |
$2$ |
$19.5560517455$ |
$59.96272324349828$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$5.44185510877$ |
3.1.7560.1 |
$x^{3} + 18 x - 16$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{3}\cdot 5\cdot 7$ |
$4$ |
$19.6263978611$ |
$60.28655668699838$ |
|
|
|
$S_3$ (as 3T2) |
$[5]$ |
$2$ |
$1$ |
$6.87631892392$ |
3.3.7668.1 |
$x^{3} - 24 x - 42$ |
$3$ |
[3,0] |
$2^{2}\cdot 3^{3}\cdot 71$ |
$3$ |
$19.7194153543$ |
$48.19004168538843$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$21.7046735703$ |
3.1.7884.1 |
$x^{3} - 18 x - 34$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{3}\cdot 73$ |
$3$ |
$19.9028623106$ |
$48.86406101606202$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$4.03840765945$ |
3.1.7884.2 |
$x^{3} + 12 x - 6$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{3}\cdot 73$ |
$3$ |
$19.9028623106$ |
$48.86406101606202$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$3.93067780292$ |
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) |
$[2]$ |
$2$ |
$1$ |
$5.70341564325$ |
3.1.8451.1 |
$x^{3} + 9 x - 70$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 313$ |
$2$ |
$20.3689840093$ |
$63.740230934284895$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$26.5330170439$ |
3.1.8532.1 |
$x^{3} + 18 x - 20$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{3}\cdot 79$ |
$3$ |
$20.4338538231$ |
$64.04496684325997$ |
|
|
|
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$3.05136186131$ |
3.1.8532.2 |
$x^{3} + 9 x - 34$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{3}\cdot 79$ |
$3$ |
$20.4338538231$ |
$64.04496684325997$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$9.84992794273$ |
3.1.8532.3 |
$x^{3} - 15 x - 42$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{3}\cdot 79$ |
$3$ |
$20.4338538231$ |
$64.04496684325997$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$11.0278163632$ |