| 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 |
| 3.3.81.1 |
$x^{3} - 3 x - 1$ |
$3$ |
[3,0] |
$3^{4}$ |
$1$ |
$4.32674871092$ |
$4.326748710922225$ |
|
✓ |
✓ |
$C_3$ (as 3T1) |
trivial |
$2$ |
$2$ |
$0.849287450646$ |
| 3.1.2835.1 |
$x^{3} - 12 x - 19$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 5\cdot 7$ |
$3$ |
$14.1530819409$ |
$25.597390575239302$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$4.31695672845$ |
| 3.1.3564.2 |
$x^{3} + 6 x - 10$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{4}\cdot 11$ |
$3$ |
$15.274930109$ |
$22.779525808351707$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$4.70782215633$ |
| 3.1.3807.1 |
$x^{3} + 15 x - 8$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 47$ |
$2$ |
$15.6144835902$ |
$29.66269470481324$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$10.2390662993$ |
| 3.1.4536.1 |
$x^{3} - 3 x - 26$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{4}\cdot 7$ |
$3$ |
$16.5535450583$ |
$32.37842254987355$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$6.90078238262$ |
| 3.1.8667.2 |
$x^{3} + 6 x - 17$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 107$ |
$2$ |
$20.5410638327$ |
$44.75623667824389$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$6.29722122909$ |
| 3.1.13284.1 |
$x^{3} + 6 x - 44$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{4}\cdot 41$ |
$3$ |
$23.6833403189$ |
$55.40941908037487$ |
|
|
|
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$3.48816749694$ |
| 3.1.16200.2 |
$x^{3} - 30 x - 80$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{4}\cdot 5^{2}$ |
$3$ |
$25.3029799591$ |
$35.783817426546634$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$15.6803908338$ |
| 3.1.18387.1 |
$x^{3} - 21 x - 64$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 227$ |
$2$ |
$26.393903551$ |
$65.18904241124454$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$13.1016442057$ |
| 3.1.19116.2 |
$x^{3} + 24 x - 28$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{4}\cdot 59$ |
$3$ |
$26.7382106608$ |
$52.75630162027896$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$7.72796099978$ |
| 3.3.20493.1 |
$x^{3} - 36 x - 9$ |
$3$ |
[3,0] |
$3^{4}\cdot 11\cdot 23$ |
$3$ |
$27.3654029034$ |
$68.82115129151201$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$14.4859990421$ |
| 3.1.21060.1 |
$x^{3} - 3 x - 28$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{4}\cdot 5\cdot 13$ |
$4$ |
$27.6154922475$ |
$69.76672663914694$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$18.4723657141$ |
| 3.3.21708.1 |
$x^{3} - 30 x - 28$ |
$3$ |
[3,0] |
$2^{2}\cdot 3^{4}\cdot 67$ |
$3$ |
$27.8958717444$ |
$70.83192910828556$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$25.9798413079$ |
| 3.1.23247.1 |
$x^{3} + 15 x - 19$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 7\cdot 41$ |
$3$ |
$28.5401097297$ |
$73.29977158861458$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$6.55810121706$ |
| 3.1.23976.1 |
$x^{3} - 9 x - 90$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{4}\cdot 37$ |
$3$ |
$28.8353732022$ |
$74.44019952022074$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$21.708678707$ |
| 3.1.25191.1 |
$x^{3} + 33 x - 98$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 311$ |
$2$ |
$29.3144535305$ |
$76.3030446359926$ |
|
|
|
$S_3$ (as 3T2) |
$[18]$ |
$2$ |
$1$ |
$5.33236865569$ |
| 3.1.26163.1 |
$x^{3} - 12 x - 35$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 17\cdot 19$ |
$3$ |
$29.6867403314$ |
$77.7611964517772$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$12.5885659222$ |
| 3.3.26325.1 |
$x^{3} - 30 x - 55$ |
$3$ |
[3,0] |
$3^{4}\cdot 5^{2}\cdot 13$ |
$3$ |
$29.7478872402$ |
$45.61559583220071$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$17.7524380017$ |
| 3.1.26892.3 |
$x^{3} + 18 x - 90$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{4}\cdot 83$ |
$3$ |
$29.9599465478$ |
$62.573058443295636$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$7.14120938804$ |
| 3.1.27864.1 |
$x^{3} + 6 x - 64$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{4}\cdot 43$ |
$3$ |
$30.3166460833$ |
$80.24923374194108$ |
|
|
|
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$5.1423811532$ |
| 3.3.32157.1 |
$x^{3} - 30 x - 53$ |
$3$ |
[3,0] |
$3^{4}\cdot 397$ |
$2$ |
$31.7998575999$ |
$86.20985732365212$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$18.7393408937$ |
| 3.1.32724.1 |
$x^{3} - 39 x - 100$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{4}\cdot 101$ |
$3$ |
$31.9856706677$ |
$86.96657277722701$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$12.0794033891$ |
| 3.3.33372.1 |
$x^{3} - 39 x - 62$ |
$3$ |
[3,0] |
$2^{2}\cdot 3^{4}\cdot 103$ |
$3$ |
$32.1954187636$ |
$87.82340699310441$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$30.8805154224$ |
| 3.1.33939.2 |
$x^{3} - 39 x - 170$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 419$ |
$2$ |
$32.3767322657$ |
$88.5663372660783$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$18.6270878267$ |
| 3.3.34344.1 |
$x^{3} - 21 x - 10$ |
$3$ |
[3,0] |
$2^{3}\cdot 3^{4}\cdot 53$ |
$3$ |
$32.5050090899$ |
$89.09320888129503$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$35.6429912739$ |
| 3.1.36612.1 |
$x^{3} + 33 x - 10$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{4}\cdot 113$ |
$3$ |
$33.2053313159$ |
$91.98793938432986$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$19.6008584665$ |
| 3.1.37827.1 |
$x^{3} + 6 x - 37$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 467$ |
$2$ |
$33.568656996$ |
$93.50183050768125$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$13.1141356163$ |
| 3.1.40743.3 |
$x^{3} + 45 x - 9$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 503$ |
$2$ |
$34.4099732215$ |
$97.03885544953614$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$7.02819907497$ |
| 3.3.40905.1 |
$x^{3} - 57 x - 161$ |
$3$ |
[3,0] |
$3^{4}\cdot 5\cdot 101$ |
$3$ |
$34.4555192353$ |
$97.23158425003115$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$15.1855750837$ |
| 3.1.42444.2 |
$x^{3} - 36 x - 252$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{4}\cdot 131$ |
$3$ |
$34.8823258977$ |
$78.61112012650996$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$10.990280197$ |
| 3.3.45036.1 |
$x^{3} - 39 x - 46$ |
$3$ |
[3,0] |
$2^{2}\cdot 3^{4}\cdot 139$ |
$3$ |
$35.5784155655$ |
$102.02322995549459$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$28.8978675123$ |
| 3.1.46575.3 |
$x^{3} + 15 x - 35$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 5^{2}\cdot 23$ |
$3$ |
$35.9791545987$ |
$60.674414460686926$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$7.61482651771$ |
| 3.1.47547.1 |
$x^{3} - 9 x - 252$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 587$ |
$2$ |
$36.2277231342$ |
$104.82882636557184$ |
|
|
|
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$6.70811539193$ |
| 3.1.48276.1 |
$x^{3} + 18 x - 252$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{4}\cdot 149$ |
$3$ |
$36.411935063$ |
$105.6293975503525$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$17.9929796741$ |
| 3.1.48519.1 |
$x^{3} + 33 x - 199$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 599$ |
$2$ |
$36.472926693$ |
$105.89490965137472$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$11.0024996505$ |
| 3.1.49491.1 |
$x^{3} - 36 x - 153$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 13\cdot 47$ |
$3$ |
$36.7148768964$ |
$106.9503667266383$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$14.4341383747$ |
| 3.1.50220.2 |
$x^{3} - 12 x - 46$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{4}\cdot 5\cdot 31$ |
$4$ |
$36.8942683939$ |
$85.50946432906022$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$16.2149249491$ |
| 3.1.51192.1 |
$x^{3} + 45 x - 234$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{4}\cdot 79$ |
$3$ |
$37.1307765728$ |
$108.77277593919919$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$25.2377713396$ |
| 3.1.51435.1 |
$x^{3} + 60 x - 125$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 5\cdot 127$ |
$3$ |
$37.1894350851$ |
$109.03063353361583$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$10.6223757885$ |
| 3.1.53379.1 |
$x^{3} - 57 x - 188$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 659$ |
$2$ |
$37.652181585$ |
$111.0719458482692$ |
|
|
|
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$4.499069481$ |
| 3.1.55323.1 |
$x^{3} + 24 x - 1$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 683$ |
$2$ |
$38.1038250236$ |
$113.0764133685715$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[18]$ |
$2$ |
$1$ |
$3.17812615523$ |
| 3.1.56052.1 |
$x^{3} + 45 x - 72$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{4}\cdot 173$ |
$3$ |
$38.2704619469$ |
$113.81898809059611$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$11.6093894795$ |
| 3.3.60345.1 |
$x^{3} - 57 x - 136$ |
$3$ |
[3,0] |
$3^{4}\cdot 5\cdot 149$ |
$3$ |
$39.2235680155$ |
$118.09725667246897$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$78.7676377604$ |
| 3.1.65772.1 |
$x^{3} - 12 x - 100$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{4}\cdot 7\cdot 29$ |
$4$ |
$40.3658110257$ |
$97.85800454964993$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$15.0574965196$ |
| 3.3.66420.1 |
$x^{3} - 48 x - 118$ |
$3$ |
[3,0] |
$2^{2}\cdot 3^{4}\cdot 5\cdot 41$ |
$4$ |
$40.4979422823$ |
$98.33888216077519$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$22.0625272224$ |
| 3.1.66987.1 |
$x^{3} - 36 x - 171$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 827$ |
$2$ |
$40.6128539626$ |
$124.4269419980067$ |
|
|
|
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$6.23441073326$ |
| 3.1.69903.3 |
$x^{3} - 9 x - 153$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 863$ |
$2$ |
$41.1938077852$ |
$127.10629824538255$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$9.34031500888$ |
| 3.1.70632.1 |
$x^{3} + 15 x - 46$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{4}\cdot 109$ |
$3$ |
$41.3365126471$ |
$127.76735828571921$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$34.4642547823$ |
| 3.1.72819.1 |
$x^{3} + 18 x - 153$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 29\cdot 31$ |
$3$ |
$41.7588218058$ |
$129.73032880677115$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$14.7949079113$ |
| 3.1.73548.1 |
$x^{3} - 30 x - 82$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{4}\cdot 227$ |
$3$ |
$41.8977102623$ |
$103.48115450040916$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3, 3]$ |
$2$ |
$1$ |
$5.27276292309$ |
