| 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 |
| 30.0.203...531.1 |
$x^{30} - x + 1$ |
$30$ |
[0,15] |
$-\,7\cdot 4547\cdot 625861750823\cdot 40306090892659\cdot 253230129277627$ |
$5$ |
$29.9874531212$ |
$1.4259153058351249e+22$ |
|
|
✓ |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$14$ |
$11086740597.223595$ |
| 30.2.208...469.1 |
$x^{30} - x - 1$ |
$30$ |
[2,14] |
$4421\cdot 22659339443160463\cdot 2080906233684319160584903$ |
$3$ |
$30.0123965237$ |
$1.4438103000318644e+22$ |
|
|
✓ |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$15$ |
$12534500381.926157$ |
| 30.2.275...081.1 |
$x^{30} - 4 x - 1$ |
$30$ |
[2,14] |
$1657\cdot 56091358577718162989\cdot 29663564839667553243668426797$ |
$3$ |
$51.8419577315$ |
$5.250744721994074e+25$ |
|
|
? |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$15$ |
$72802108759548.89$ |
| 30.2.275...456.1 |
$x^{30} - 2 x - 1$ |
$30$ |
[2,14] |
$2^{31}\cdot 309259\cdot 14808181703558627\cdot 280341823437737461079$ |
$4$ |
$51.8419578606$ |
|
|
|
✓ |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$15$ |
$90634957909906.56$ |
| 30.0.525...544.1 |
$x^{30} - 4 x + 4$ |
$30$ |
[0,15] |
$-\,2^{30}\cdot 23\cdot 21\!\cdots\!97$ |
$3$ |
$57.1928580583$ |
|
|
|
? |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$14$ |
$552056500614525.9$ |
| 30.2.580...456.1 |
$x^{30} - 4 x - 4$ |
$30$ |
[2,14] |
$2^{30}\cdot 11\cdot 19\cdot 163\cdot 1523\cdot 192007\cdot 2905267\cdot 16453379\cdot 331846583\cdot 341971373$ |
$10$ |
$57.3835351014$ |
|
|
|
? |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$15$ |
$474936634338780.94$ |
| 30.0.107...544.1 |
$x^{30} - 2 x + 2$ |
$30$ |
[0,15] |
$-\,2^{30}\cdot 4261\cdot 1538746509977\cdot 15309443470070730473327119823$ |
$4$ |
$58.5802556901$ |
|
|
|
✓ |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$14$ |
$570084675612509.6$ |
| 30.0.110...531.1 |
$x^{30} - x + 2$ |
$30$ |
[0,15] |
$-\,16069\cdot 68\!\cdots\!99$ |
$2$ |
$58.629598106$ |
$3.324709910019203e+26$ |
|
|
✓ |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$14$ |
$860909290548142.0$ |
| 30.2.113...456.1 |
$x^{30} - 2 x - 2$ |
$30$ |
[2,14] |
$2^{30}\cdot 31\cdot 1493\cdot 294391\cdot 77\!\cdots\!73$ |
$5$ |
$58.6777648873$ |
|
|
|
✓ |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$15$ |
$787485177668371.2$ |
| 30.2.528...381.1 |
$x^{30} - 3 x + 1$ |
$30$ |
[2,14] |
$3^{30}\cdot 7\cdot 83\cdot 547\cdot 80\!\cdots\!67$ |
$5$ |
$77.7629365973$ |
|
|
|
✓ |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$15$ |
$27174736235759336$ |
| 30.2.528...381.1 |
$x^{30} - 3 x - 1$ |
$30$ |
[2,14] |
$3^{31}\cdot 2579\cdot 3847572842487629\cdot 86254644893658285239753$ |
$4$ |
$77.7629365973$ |
|
|
|
✓ |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$15$ |
$31296766042731750$ |
| 30.2.528...381.1 |
$x^{30} - 3 x - 2$ |
$30$ |
[2,14] |
$3^{30}\cdot 31\cdot 1769381441963\cdot 46821958249121311829160660473$ |
$4$ |
$77.7634785176$ |
|
|
|
✓ |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$15$ |
$96404046034030270$ |
| 30.0.136...619.1 |
$x^{30} - 3 x + 3$ |
$30$ |
[0,15] |
$-\,3^{30}\cdot 13\cdot 50\!\cdots\!87$ |
$3$ |
$86.6535707438$ |
|
|
|
✓ |
$S_{30}$ (as 30T5712) |
$[2]$ |
$2$ |
$14$ |
$56438497078123610$ |
| 30.0.141...544.1 |
$x^{30} - 2 x + 3$ |
$30$ |
[0,15] |
$-\,2^{31}\cdot 4447\cdot 21434117\cdot 86927089867957\cdot 794138426549944803348421$ |
$5$ |
$86.7637800633$ |
|
|
|
✓ |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$14$ |
$387750706553255400$ |
| 30.0.141...531.1 |
$x^{30} - x + 3$ |
$30$ |
[0,15] |
$-\,13\cdot 179\cdot 560893979\cdot 1599364314633798641\cdot 6769077172765732520137982927$ |
$5$ |
$86.7637806276$ |
$1.1887130053860239e+29$ |
|
|
✓ |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$14$ |
$256499963343328640$ |
| 30.2.141...469.1 |
$x^{30} - x - 3$ |
$30$ |
[2,14] |
$277\cdot 400264301\cdot 5331180702097\cdot 132214342318352251\cdot 180811241978611351$ |
$5$ |
$86.7637806276$ |
$1.188713005386024e+29$ |
|
|
✓ |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$15$ |
$275535081946504500$ |
| 30.2.146...381.1 |
$x^{30} - 3 x - 3$ |
$30$ |
[2,14] |
$3^{30}\cdot 883\cdot 468509\cdot 30594564677969\cdot 5625294473757709912283$ |
$5$ |
$86.8700745284$ |
|
|
|
✓ |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$15$ |
$210282023224939900$ |
| 30.2.490...789.1 |
$x^{30} - x - 4$ |
$30$ |
[2,14] |
$313\cdot 1553\cdot 2467\cdot 40\!\cdots\!03$ |
$4$ |
$97.6531823256$ |
$7.003191624811985e+29$ |
|
|
? |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$15$ |
$2013910243703532000$ |
| 30.2.296...744.1 |
$x^{30} - 4 x + 2$ |
$30$ |
[2,14] |
$2^{59}\cdot 1847\cdot 15727\cdot 398407\cdot 551671\cdot 2918921\cdot 275568568450197721$ |
$7$ |
$103.683915334$ |
|
|
|
✓ |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$15$ |
$2871305700797111000$ |
| 30.2.296...744.1 |
$x^{30} - 4 x + 1$ |
$30$ |
[2,14] |
$2^{30}\cdot 7\cdot 149\cdot 8329\cdot 14869697\cdot 24084784266299\cdot 886175540693210057361991$ |
$7$ |
$103.683915463$ |
|
|
|
✓ |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$15$ |
$7912688478084103000$ |
| 30.2.296...744.1 |
$x^{30} - 4 x - 2$ |
$30$ |
[2,14] |
$2^{59}\cdot 31\cdot 101\cdot 36470152085223887711\cdot 44972943052468912543$ |
$5$ |
$103.683915592$ |
|
|
|
✓ |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$15$ |
$9880263253170928000$ |
| 30.2.297...744.1 |
$x^{30} - 4 x - 3$ |
$30$ |
[2,14] |
$2^{30}\cdot 47\cdot 113\cdot 70468441\cdot 118739592888857\cdot 62336633454993137535840733$ |
$6$ |
$103.700374428$ |
|
|
|
✓ |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$15$ |
$10204871904021840000$ |
| 30.0.148...136.1 |
$x^{30} - 2 x + 4$ |
$30$ |
[0,15] |
$-\,2^{28}\cdot 4899563\cdot 468731357\cdot 5400051347\cdot 4456544800255361855961256703$ |
$5$ |
$109.406698627$ |
$4.590800402718109e+26$ |
|
|
? |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$14$ |
$16701494058586538000$ |
| 30.2.148...864.1 |
$x^{30} - 2 x - 4$ |
$30$ |
[2,14] |
$2^{28}\cdot 11\cdot 2579\cdot 19\!\cdots\!01$ |
$4$ |
$109.406698627$ |
$4.5908004029313905e+26$ |
|
|
? |
$S_{30}$ (as 30T5712) |
not computed |
$2$ |
$15$ |
|
| 30.2.522...872.1 |
$x^{30} - 3 x^{29} + 6 x^{28} - 10 x^{27} + 15 x^{26} - 21 x^{25} + 28 x^{24} - 36 x^{23} + 45 x^{22} - 55 x^{21} + 66 x^{20} - 78 x^{19} + 91 x^{18} + 1623 x^{17} - 5064 x^{16} + 10232 x^{15} - 17127 x^{14} + 25749 x^{13} - 36098 x^{12} + 48174 x^{11} - 117273 x^{10} + 243395 x^{9} - 426540 x^{8} + 666708 x^{7} - 963899 x^{6} + 1318113 x^{5} - 1321110 x^{4} + 1235034 x^{3} - 1059885 x^{2} + 795663 x - 442368$ |
$30$ |
[2,14] |
$2^{102}\cdot 3^{65}$ |
$2$ |
$114.09449851398588$ |
|
|
|
|
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$15$ |
$522479778434043400000$ |
| 30.0.593...619.1 |
$x^{30} - 3 x + 4$ |
$30$ |
[0,15] |
$-\,3^{30}\cdot 4329008673689392661\cdot 66580556933815696116855581671$ |
$3$ |
$114.580958444$ |
|
|
|
✓ |
$S_{30}$ (as 30T5712) |
$[2]$ |
$2$ |
$14$ |
$9555863009872810000$ |
| 30.0.593...531.1 |
$x^{30} - x + 4$ |
$30$ |
[0,15] |
$-\,288817\cdot 111899407981\cdot 6492534437104925213\cdot 282821607796117415613307931$ |
$4$ |
$114.580992469$ |
$7.703510787293184e+30$ |
|
|
✓ |
$S_{30}$ (as 30T5712) |
$[2]$ |
$2$ |
$14$ |
$15641356780346671000$ |
| 30.2.239...125.1 |
$x^{30} - 5 x + 3$ |
$30$ |
[2,14] |
$5^{30}\cdot 21713739362807\cdot 118250980997440906149013156123$ |
$3$ |
$129.604868801$ |
|
|
|
✓ |
$S_{30}$ (as 30T5712) |
not computed |
$2$ |
$15$ |
|
| 30.2.239...125.1 |
$x^{30} - 5 x + 2$ |
$30$ |
[2,14] |
$5^{30}\cdot 167\cdot 2357\cdot 6094873\cdot 26805343\cdot 39928211377608794948777$ |
$6$ |
$129.604894329$ |
|
|
|
✓ |
$S_{30}$ (as 30T5712) |
not computed |
$2$ |
$15$ |
|
| 30.2.239...125.1 |
$x^{30} - 5 x + 1$ |
$30$ |
[2,14] |
$5^{30}\cdot 7\cdot 5801\cdot 3546119\cdot 17\!\cdots\!21$ |
$5$ |
$129.604894329$ |
|
|
|
✓ |
$S_{30}$ (as 30T5712) |
not computed |
$2$ |
$15$ |
|
| 30.2.239...125.1 |
$x^{30} - 5 x - 1$ |
$30$ |
[2,14] |
$5^{31}\cdot 10309974007\cdot 49\!\cdots\!07$ |
$3$ |
$129.604894329$ |
|
|
|
✓ |
$S_{30}$ (as 30T5712) |
not computed |
$2$ |
$15$ |
|
| 30.2.239...125.1 |
$x^{30} - 5 x - 2$ |
$30$ |
[2,14] |
$5^{30}\cdot 31\cdot 43441\cdot 19\!\cdots\!11$ |
$4$ |
$129.604894329$ |
|
|
|
✓ |
$S_{30}$ (as 30T5712) |
not computed |
$2$ |
$15$ |
|
| 30.2.239...125.1 |
$x^{30} - 5 x - 3$ |
$30$ |
[2,14] |
$5^{30}\cdot 13\cdot 5801281\cdot 34\!\cdots\!09$ |
$4$ |
$129.604919856$ |
|
|
|
✓ |
$S_{30}$ (as 30T5712) |
not computed |
$2$ |
$15$ |
|
| 30.2.245...125.1 |
$x^{30} - 5 x - 4$ |
$30$ |
[2,14] |
$5^{30}\cdot 11\cdot 839\cdot 1871\cdot 2027569\cdot 75159493718018483766865870303$ |
$6$ |
$129.710838983$ |
|
|
|
✓ |
$S_{30}$ (as 30T5712) |
not computed |
$2$ |
$15$ |
|
| 30.0.426...291.1 |
$x^{30} - 3 x + 5$ |
$30$ |
[0,15] |
$-\,3^{29}\cdot 71\cdot 467\cdot 51628578737\cdot 9899468832468151\cdot 3663798440144491003$ |
$6$ |
$132.124748935$ |
|
|
|
? |
$S_{30}$ (as 30T5712) |
not computed |
$2$ |
$14$ |
|
| 30.0.958...136.1 |
$x^{30} - 2 x + 5$ |
$30$ |
[0,15] |
$-\,2^{31}\cdot 27697516504717\cdot 16\!\cdots\!21$ |
$3$ |
$135.744922072$ |
|
|
|
? |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$14$ |
$316128619265654000000$ |
| 30.0.359...875.1 |
$x^{30} - 5 x + 5$ |
$30$ |
[0,15] |
$-\,5^{30}\cdot 22824228476857\cdot 16\!\cdots\!83$ |
$3$ |
$141.860079955$ |
|
|
|
✓ |
$S_{30}$ (as 30T5712) |
not computed |
$2$ |
$14$ |
|
| 30.0.383...256.1 |
$x^{30} - 4 x + 5$ |
$30$ |
[0,15] |
$-\,2^{30}\cdot 71\cdot 109\cdot 128047\cdot 65725731723640882837\cdot 548333383871954330575047389$ |
$6$ |
$142.164493274$ |
|
|
|
✓ |
$S_{30}$ (as 30T5712) |
not computed |
$2$ |
$14$ |
|
| 30.0.383...531.1 |
$x^{30} - x + 5$ |
$30$ |
[0,15] |
$-\,17\cdot 47\cdot 16981\cdot 28\!\cdots\!49$ |
$4$ |
$142.164859088$ |
$1.958321011646886e+32$ |
|
|
✓ |
$S_{30}$ (as 30T5712) |
not computed |
$2$ |
$14$ |
|
| 30.2.383...469.1 |
$x^{30} - x - 5$ |
$30$ |
[2,14] |
$23\cdot 107\cdot 352188553406401\cdot 44\!\cdots\!29$ |
$4$ |
$142.164859088$ |
$1.958321011646886e+32$ |
|
|
✓ |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$15$ |
$540288053755210240000$ |
| 30.2.383...456.1 |
$x^{30} - 2 x - 5$ |
$30$ |
[2,14] |
$2^{31}\cdot 49823\cdot 4049666919614429899\cdot 88\!\cdots\!61$ |
$4$ |
$142.164859088$ |
|
|
|
✓ |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$15$ |
$1612248364188678200000$ |
| 30.2.383...381.1 |
$x^{30} - 3 x - 5$ |
$30$ |
[2,14] |
$3^{30}\cdot 2477\cdot 75\!\cdots\!97$ |
$3$ |
$142.164859154$ |
|
|
|
✓ |
$S_{30}$ (as 30T5712) |
not computed |
$2$ |
$15$ |
|
| 30.2.407...125.1 |
$x^{30} - 5 x - 5$ |
$30$ |
[2,14] |
$5^{30}\cdot 5217677\cdot 83\!\cdots\!97$ |
$3$ |
$142.451793134$ |
|
|
|
✓ |
$S_{30}$ (as 30T5712) |
$[2]$ |
$2$ |
$15$ |
$190324083555344740000$ |
