| 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 |
| 3.1.891.1 |
$x^{3} + 6 x - 1$ |
$3$ |
(1, 1) |
$-\,3^{4}\cdot 11$ |
$2$ |
$9.62260298999$ |
$14.350202036282921$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$1.79633642278$ |
| 3.1.1620.1 |
$x^{3} - 3 x - 8$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3^{4}\cdot 5$ |
$3$ |
$11.7446029235$ |
$19.349808478363364$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$4.13933789115$ |
| 3.3.3969.1 |
$x^{3} - 21 x - 28$ |
$3$ |
(3, 0) |
$3^{4}\cdot 7^{2}$ |
$2$ |
$15.8328962637$ |
$15.83289626371223$ |
|
✓ |
|
$C_3$ (as 3T1) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$12.5941889569$ |
| 3.3.4212.1 |
$x^{3} - 12 x - 10$ |
$3$ |
(3, 0) |
$2^{2}\cdot 3^{4}\cdot 13$ |
$3$ |
$16.1496378363$ |
$24.76395538367976$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[6]$ |
$2$ |
$2$ |
$5.45742079518$ |
| 3.1.5508.1 |
$x^{3} + 6 x - 28$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3^{4}\cdot 17$ |
$3$ |
$17.6602959507$ |
$35.67928390127477$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$8.73632848908$ |
| 3.1.5751.1 |
$x^{3} - 9 x - 45$ |
$3$ |
(1, 1) |
$-\,3^{4}\cdot 71$ |
$2$ |
$17.9162778595$ |
$36.45783266912841$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$3.49653538601$ |
| 3.1.8667.1 |
$x^{3} + 18 x - 45$ |
$3$ |
(1, 1) |
$-\,3^{4}\cdot 107$ |
$2$ |
$20.5410638327$ |
$44.75623667824389$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$[6]$ |
$2$ |
$1$ |
$3.40783442259$ |
| 3.1.9639.1 |
$x^{3} - 3 x - 19$ |
$3$ |
(1, 1) |
$-\,3^{4}\cdot 7\cdot 17$ |
$3$ |
$21.2819128343$ |
$47.19925607982174$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$3.19339289157$ |
| 3.1.11340.1 |
$x^{3} - 12 x - 44$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3^{4}\cdot 5\cdot 7$ |
$4$ |
$22.4666171617$ |
$40.63332472677574$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$8.42045574104$ |
| 3.3.13689.2 |
$x^{3} - 39 x - 91$ |
$3$ |
(3, 0) |
$3^{4}\cdot 13^{2}$ |
$2$ |
$23.9216192981$ |
$23.921619298064325$ |
|
✓ |
✓ |
$C_3$ (as 3T1) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$5.61392117258$ |
| 3.3.14661.1 |
$x^{3} - 36 x - 45$ |
$3$ |
(3, 0) |
$3^{4}\cdot 181$ |
$2$ |
$24.4749153223$ |
$58.21045050290842$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$15.838693992$ |
| 3.1.16200.1 |
$x^{3} + 15 x - 10$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 3^{4}\cdot 5^{2}$ |
$3$ |
$25.3029799591$ |
$35.783817426546634$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$13.4584826974$ |
| 3.1.16443.1 |
$x^{3} + 15 x - 44$ |
$3$ |
(1, 1) |
$-\,3^{4}\cdot 7\cdot 29$ |
$3$ |
$25.4288675037$ |
$61.646679916406114$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$10.063051697$ |
| 3.1.17415.1 |
$x^{3} - 3 x - 127$ |
$3$ |
(1, 1) |
$-\,3^{4}\cdot 5\cdot 43$ |
$3$ |
$25.9203677931$ |
$63.442589776942704$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$4.14614848906$ |
| 3.3.18792.1 |
$x^{3} - 21 x - 26$ |
$3$ |
(3, 0) |
$2^{3}\cdot 3^{4}\cdot 29$ |
$3$ |
$26.5862857302$ |
$65.90307293694563$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[6]$ |
$2$ |
$2$ |
$19.3897303111$ |
| 3.1.19116.1 |
$x^{3} + 6 x - 26$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3^{4}\cdot 59$ |
$3$ |
$26.7382106608$ |
$52.75630162027896$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$5.38863368158$ |
| 3.1.20331.1 |
$x^{3} + 33 x - 82$ |
$3$ |
(1, 1) |
$-\,3^{4}\cdot 251$ |
$2$ |
$27.2931029552$ |
$68.54859120561305$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$8.27868970364$ |
| 3.1.21303.1 |
$x^{3} + 15 x - 17$ |
$3$ |
(1, 1) |
$-\,3^{4}\cdot 263$ |
$2$ |
$27.7212997648$ |
$70.1680725769481$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$[6]$ |
$2$ |
$1$ |
$2.89967026199$ |
| 3.3.26568.1 |
$x^{3} - 30 x - 8$ |
$3$ |
(3, 0) |
$2^{3}\cdot 3^{4}\cdot 41$ |
$3$ |
$29.8391389996$ |
$78.36075194668068$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[6]$ |
$2$ |
$2$ |
$26.9643567724$ |
| 3.1.26892.1 |
$x^{3} - 36 x - 126$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3^{4}\cdot 83$ |
$3$ |
$29.9599465478$ |
$62.573058443295636$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$11.5007212958$ |
| 3.3.29241.2 |
$x^{3} - 57 x - 19$ |
$3$ |
(3, 0) |
$3^{4}\cdot 19^{2}$ |
$2$ |
$30.8080402914$ |
$30.80804029142189$ |
|
✓ |
|
$C_3$ (as 3T1) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$9.7184036612$ |
| 3.1.30051.1 |
$x^{3} - 12 x - 37$ |
$3$ |
(1, 1) |
$-\,3^{4}\cdot 7\cdot 53$ |
$3$ |
$31.0899227421$ |
$83.33906578052282$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$[6]$ |
$2$ |
$1$ |
$5.27228887717$ |
| 3.1.31023.1 |
$x^{3} + 15 x - 64$ |
$3$ |
(1, 1) |
$-\,3^{4}\cdot 383$ |
$2$ |
$31.4215736093$ |
$84.676141492512$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$33.6986824643$ |
| 3.1.32967.1 |
$x^{3} - 3 x - 35$ |
$3$ |
(1, 1) |
$-\,3^{4}\cdot 11\cdot 37$ |
$3$ |
$32.0646479529$ |
$87.28887124851097$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$7.06215197975$ |
| 3.1.33939.3 |
$x^{3} - 21 x - 80$ |
$3$ |
(1, 1) |
$-\,3^{4}\cdot 419$ |
$2$ |
$32.3767322657$ |
$88.5663372660783$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$17.3601112442$ |
| 3.1.35883.1 |
$x^{3} - 30 x - 73$ |
$3$ |
(1, 1) |
$-\,3^{4}\cdot 443$ |
$2$ |
$32.9834627885$ |
$91.06752550996399$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$14.763102263$ |
| 3.3.37017.1 |
$x^{3} - 21 x - 1$ |
$3$ |
(3, 0) |
$3^{4}\cdot 457$ |
$2$ |
$33.3273211379$ |
$92.49532293155413$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$12.5394048054$ |
| 3.1.38799.1 |
$x^{3} - 21 x - 53$ |
$3$ |
(1, 1) |
$-\,3^{4}\cdot 479$ |
$2$ |
$33.8537547826$ |
$94.6955192243897$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$4.94876024711$ |
| 3.1.39528.1 |
$x^{3} - 57 x - 170$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 3^{4}\cdot 61$ |
$3$ |
$34.0644682251$ |
$95.58100308557115$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$[6]$ |
$2$ |
$1$ |
$10.6984918033$ |
| 3.1.40743.2 |
$x^{3} - 9 x - 117$ |
$3$ |
(1, 1) |
$-\,3^{4}\cdot 503$ |
$2$ |
$34.4099732215$ |
$97.03885544953614$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$5.79026867269$ |
| 3.1.42444.1 |
$x^{3} - 48 x - 134$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3^{4}\cdot 131$ |
$3$ |
$34.8823258977$ |
$78.61112012650996$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$5.6732878788$ |
| 3.1.43416.1 |
$x^{3} + 6 x - 80$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 3^{4}\cdot 67$ |
$3$ |
$35.1465960159$ |
$100.17147479398706$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$28.8936167941$ |
| 3.1.44388.1 |
$x^{3} + 45 x - 36$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3^{4}\cdot 137$ |
$3$ |
$35.4069506605$ |
$101.28659050087525$ |
|
|
|
$S_3$ (as 3T2) |
$[12]$ |
$[12]$ |
$2$ |
$1$ |
$5.69335785543$ |
| 3.1.44631.1 |
$x^{3} - 21 x - 55$ |
$3$ |
(1, 1) |
$-\,3^{4}\cdot 19\cdot 29$ |
$3$ |
$35.4714443379$ |
$101.56345641279836$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$[6]$ |
$2$ |
$1$ |
$6.46920705108$ |
| 3.1.46575.1 |
$x^{3} + 45 x - 45$ |
$3$ |
(1, 1) |
$-\,3^{4}\cdot 5^{2}\cdot 23$ |
$3$ |
$35.9791545987$ |
$60.674414460686926$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$[6]$ |
$2$ |
$1$ |
$3.86990546642$ |
| 3.1.47304.1 |
$x^{3} - 9 x - 126$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 3^{4}\cdot 73$ |
$3$ |
$36.1659009609$ |
$104.56060718052859$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$[6]$ |
$2$ |
$1$ |
$11.7985930423$ |
| 3.1.50220.1 |
$x^{3} + 18 x - 126$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3^{4}\cdot 5\cdot 31$ |
$4$ |
$36.8942683939$ |
$85.50946432906022$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$16.5087356075$ |
| 3.1.50463.1 |
$x^{3} + 15 x - 37$ |
$3$ |
(1, 1) |
$-\,3^{4}\cdot 7\cdot 89$ |
$3$ |
$36.9536795568$ |
$107.9955091466864$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$[6]$ |
$2$ |
$1$ |
$3.28755542743$ |
| 3.3.50868.1 |
$x^{3} - 30 x - 46$ |
$3$ |
(3, 0) |
$2^{2}\cdot 3^{4}\cdot 157$ |
$3$ |
$37.0522757539$ |
$86.05937008852867$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$18.166876891$ |
| 3.1.62127.1 |
$x^{3} - 9 x - 288$ |
$3$ |
(1, 1) |
$-\,3^{4}\cdot 13\cdot 59$ |
$3$ |
$39.6059219794$ |
$119.82828810647048$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$50.6770119792$ |
| 3.1.62856.1 |
$x^{3} + 18 x - 288$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 3^{4}\cdot 97$ |
$3$ |
$39.7602323249$ |
$120.52927204706124$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$16.684424229$ |
| 3.1.63828.1 |
$x^{3} - 30 x - 116$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3^{4}\cdot 197$ |
$3$ |
$39.964134518$ |
$121.45762418672656$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$26.9529037226$ |
| 3.1.65043.1 |
$x^{3} + 24 x - 19$ |
$3$ |
(1, 1) |
$-\,3^{4}\cdot 11\cdot 73$ |
$3$ |
$40.2161218473$ |
$122.60817994406455$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$15.7213805496$ |
| 3.1.69903.2 |
$x^{3} + 33 x - 190$ |
$3$ |
(1, 1) |
$-\,3^{4}\cdot 863$ |
$2$ |
$41.1938077852$ |
$127.10629824538255$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$57.1346665789$ |
| 3.3.70065.1 |
$x^{3} - 63 x - 117$ |
$3$ |
(3, 0) |
$3^{4}\cdot 5\cdot 173$ |
$3$ |
$41.225605411$ |
$127.25349725040594$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[6]$ |
$2$ |
$2$ |
$13.498132941$ |
| 3.3.74925.1 |
$x^{3} - 30 x - 35$ |
$3$ |
(3, 0) |
$3^{4}\cdot 5^{2}\cdot 37$ |
$3$ |
$42.1575713657$ |
$76.9560091999056$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[6]$ |
$2$ |
$2$ |
$36.0735066735$ |
| 3.1.76707.1 |
$x^{3} + 6 x - 53$ |
$3$ |
(1, 1) |
$-\,3^{4}\cdot 947$ |
$2$ |
$42.4891783289$ |
$133.14861780683785$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$20.8862086683$ |
| 3.3.77841.2 |
$x^{3} - 93 x - 341$ |
$3$ |
(3, 0) |
$3^{4}\cdot 31^{2}$ |
$2$ |
$42.6975348997$ |
$42.697534899657064$ |
|
✓ |
✓ |
$C_3$ (as 3T1) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$7.89983233866$ |
| 3.3.80028.1 |
$x^{3} - 75 x - 244$ |
$3$ |
(3, 0) |
$2^{2}\cdot 3^{4}\cdot 13\cdot 19$ |
$4$ |
$43.0937202285$ |
$136.00038733245407$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$45.3576304378$ |
| 3.3.80757.1 |
$x^{3} - 66 x - 199$ |
$3$ |
(3, 0) |
$3^{4}\cdot 997$ |
$2$ |
$43.2241762824$ |
$136.6184180271633$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$31.9300034046$ |
