| 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 |
| 15.1.723352547563839.1 |
$x^{15} - x^{14} - 2 x^{13} + 2 x^{12} - 2 x^{11} + 2 x^{10} + 5 x^{9} - 5 x^{8} + 4 x^{7} - 5 x^{6} - 4 x^{5} + 5 x^{4} - 2 x^{3} + x^{2} + x + 1$ |
$15$ |
[1,7] |
$-\,3^{3}\cdot 6653\cdot 4026880369$ |
$3$ |
$9.78640837431$ |
$8965071.404337559$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$11.7410590074$ |
| 15.3.2164169497031757.1 |
$x^{15} - 7 x^{14} + 23 x^{13} - 45 x^{12} + 54 x^{11} - 32 x^{10} - 14 x^{9} + 55 x^{8} - 72 x^{7} + 69 x^{6} - 57 x^{5} + 39 x^{4} - 21 x^{3} + 9 x^{2} - 4 x + 1$ |
$15$ |
[3,6] |
$3^{3}\cdot 69593\cdot 1151759887$ |
$3$ |
$10.5281666665$ |
$15506878.391474314$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$8$ |
$29.6657425505$ |
| 15.3.2354315214908549.1 |
$x^{15} - x^{14} + x^{13} - x^{12} - x^{11} + 3 x^{10} - 2 x^{9} + 2 x^{8} - 2 x^{7} - x^{6} + 2 x^{3} - x^{2} + 2 x - 1$ |
$15$ |
[3,6] |
$27765763\cdot 84792023$ |
$2$ |
$10.5874402875$ |
$48521286.204186186$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$8$ |
$31.1653663197$ |
| 15.3.3276367268581097.1 |
$x^{15} - 6 x^{13} - x^{12} + 16 x^{11} + 8 x^{10} - 20 x^{9} - 24 x^{8} + 4 x^{7} + 31 x^{6} + 15 x^{5} - 15 x^{4} - 14 x^{3} + x^{2} + 4 x + 1$ |
$15$ |
[3,6] |
$3276367268581097$ |
$1$ |
$10.8232952365$ |
$57239560.34580539$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$8$ |
$37.7909873347$ |
| 15.1.3703260525677583.1 |
$x^{15} - 2 x^{14} + x^{13} - x^{12} - 5 x^{11} + 4 x^{10} - 3 x^{9} + 2 x^{8} + 6 x^{7} - 3 x^{6} + 3 x^{5} - 4 x^{4} - 5 x^{3} - 3 x^{2} - 3 x - 1$ |
$15$ |
[1,7] |
$-\,3\cdot 13^{3}\cdot 561866260913$ |
$3$ |
$10.912031669$ |
$8888625.705547903$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$39.9823344692$ |
| 15.1.5976545641547631.1 |
$x^{15} - 2 x^{14} + 5 x^{13} - 10 x^{12} + 13 x^{11} - 20 x^{10} + 23 x^{9} - 22 x^{8} + 22 x^{7} - 20 x^{6} + 18 x^{5} - 20 x^{4} + 21 x^{3} - 15 x^{2} + 6 x - 1$ |
$15$ |
[1,7] |
$-\,3\cdot 195479\cdot 10191283363$ |
$3$ |
$11.2658340433$ |
$77308121.44624671$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$50.8430332143$ |
| 15.3.6114596477365737.1 |
$x^{15} - 3 x^{14} + 5 x^{13} - 2 x^{12} - 8 x^{11} + 18 x^{10} - 18 x^{9} + 20 x^{7} - 27 x^{6} + 15 x^{5} + 3 x^{4} - 11 x^{3} + 10 x^{2} - 5 x + 1$ |
$15$ |
[3,6] |
$3^{4}\cdot 15601\cdot 4838718377$ |
$3$ |
$11.2829982327$ |
$15048805.141895186$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$8$ |
$53.4601866446$ |
| 15.5.10496055636998343.1 |
$x^{15} - 4 x^{14} + 6 x^{13} - x^{12} - 11 x^{11} + 18 x^{10} - 10 x^{9} - 9 x^{8} + 19 x^{7} - 12 x^{6} - 3 x^{5} + 9 x^{4} - 5 x^{3} - x^{2} + 3 x - 1$ |
$15$ |
[5,5] |
$-\,3^{5}\cdot 157\cdot 2377\cdot 115742009$ |
$4$ |
$11.6968362025$ |
$11383362.147893872$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$9$ |
$99.2990074596$ |
| 15.3.12853809661090929.1 |
$x^{15} - x^{14} - x^{13} + 3 x^{12} - x^{10} - 4 x^{9} + 4 x^{8} + 2 x^{7} - 7 x^{6} - x^{5} + 2 x^{4} - x^{3} + 2 x + 1$ |
$15$ |
[3,6] |
$3\cdot 4284603220363643$ |
$2$ |
$11.855925391$ |
$113374642.9369942$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$8$ |
$108.091851993$ |
| 15.3.16680932154277329.1 |
$x^{15} - 2 x^{14} + 6 x^{13} - 14 x^{12} + 23 x^{11} - 35 x^{10} + 44 x^{9} - 41 x^{8} + 25 x^{7} - 4 x^{6} - 20 x^{5} + 34 x^{4} - 30 x^{3} + 17 x^{2} - 6 x + 1$ |
$15$ |
[3,6] |
$3\cdot 47\cdot 103\cdot 11057\cdot 103878739$ |
$5$ |
$12.063722938$ |
$129154683.05205712$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$8$ |
$124.641970008$ |
| 15.5.77595502265817783.1 |
$x^{15} - 3 x^{13} - 2 x^{12} + x^{11} + 12 x^{10} + 3 x^{9} - 15 x^{8} - 10 x^{7} - 4 x^{6} + 20 x^{5} + 7 x^{4} - 3 x^{3} - 7 x^{2} - 4 x + 1$ |
$15$ |
[5,5] |
$-\,3\cdot 13^{3}\cdot 11772948303113$ |
$3$ |
$13.3656198083$ |
$40687476.96822902$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$9$ |
$416.964032767$ |
| 15.1.426781883555301359.1 |
$x^{15} - x - 1$ |
$15$ |
[1,7] |
$-\,52489\cdot 418511\cdot 19428121$ |
$3$ |
$14.9743184596$ |
$653285453.3473873$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$501.532588967$ |
| 15.1.449005897206417391.1 |
$x^{15} + x - 1$ |
$15$ |
[1,7] |
$-\,7334881\cdot 61215157711$ |
$2$ |
$15.0250803442$ |
$670079023.1057956$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$548.874139448$ |
| 15.5.109...839.1 |
$x^{15} - 4 x^{14} + 9 x^{13} - 7 x^{12} - 10 x^{11} + 31 x^{10} - 21 x^{9} - 32 x^{8} + 45 x^{7} + 13 x^{6} - 35 x^{5} - 2 x^{4} + 12 x^{3} - 3 x^{2} - 5 x - 1$ |
$15$ |
[5,5] |
$-\,3^{2}\cdot 121558348928602871$ |
$2$ |
$15.9441664713$ |
$603883305.6028364$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$9$ |
$2377.94441595$ |
| 15.1.219...096.1 |
$x^{15} - 2 x^{14} + 5 x^{12} - 8 x^{11} + 2 x^{10} + 9 x^{9} - 11 x^{8} + 11 x^{6} - 7 x^{5} - 3 x^{4} + 7 x^{3} - x^{2} - 2 x + 1$ |
$15$ |
[1,7] |
$-\,2^{6}\cdot 34304987175946939$ |
$2$ |
$16.7020257541$ |
$523870115.0166666$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$2000.14922252$ |
| 15.3.665...153.1 |
$x^{15} - 2 x^{14} + 4 x^{13} - 6 x^{12} + 7 x^{11} - 7 x^{10} + 5 x^{9} - 3 x^{8} - x^{7} + 4 x^{6} - 5 x^{5} + 4 x^{4} - 3 x^{3} + x - 1$ |
$15$ |
[3,6] |
$33479\cdot 37871\cdot 69401\cdot 75617$ |
$4$ |
$17.9833651002$ |
$2579480273.582714$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$8$ |
$5504.77056814$ |
| 15.3.774...572.1 |
$x^{15} - 2 x^{14} + 5 x^{12} - 8 x^{11} + 2 x^{10} + 9 x^{9} - 10 x^{8} + 11 x^{6} - 7 x^{5} - 3 x^{4} + 7 x^{3} - 2 x^{2} - 2 x + 1$ |
$15$ |
[3,6] |
$2^{2}\cdot 62896103\cdot 30801208681$ |
$3$ |
$18.1670090503$ |
|
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$8$ |
$4178.0205499$ |
| 15.1.364...663.1 |
$x^{15} + 2 x - 1$ |
$15$ |
[1,7] |
$-\,999381407\cdot 364781785009$ |
$2$ |
$23.4846609148$ |
$19093353124.851223$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$34283.3529428$ |
| 15.1.142...712.1 |
$x^{15} - 5 x^{12} + 10 x^{9} - 10 x^{6} + 5 x^{3} - 2 x - 1$ |
$15$ |
[1,7] |
$-\,2^{12}\cdot 13\cdot 103\cdot 13063\cdot 14747\cdot 1352993$ |
$6$ |
$25.7244152891$ |
$1028573576.719291$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$131527.777073$ |
| 15.1.203...031.1 |
$x^{15} + 4 x - 3$ |
$15$ |
[1,7] |
$-\,443\cdot 4103689\cdot 1119940962053$ |
$3$ |
$26.3381269343$ |
$45121824067.023895$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$132292.270091$ |
| 15.1.215...288.1 |
$x^{15} - 5 x^{12} + 10 x^{9} - 10 x^{6} + 5 x^{3} + 2 x - 1$ |
$15$ |
[1,7] |
$-\,2^{12}\cdot 11\cdot 37\cdot 3659\cdot 353737138331$ |
$5$ |
$26.4403070929$ |
$1263696361.2239738$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$86426.3966059$ |
| 15.1.644...424.1 |
$x^{15} - 4 x - 4$ |
$15$ |
[1,7] |
$-\,2^{14}\cdot 17\cdot 71\cdot 325970060545673$ |
$4$ |
$28.4415762438$ |
$1197853816.455049$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$119442.750061$ |
| 15.1.681...712.1 |
$x^{15} - 2 x - 2$ |
$15$ |
[1,7] |
$-\,2^{14}\cdot 6737\cdot 61699551243839$ |
$3$ |
$28.5459542966$ |
$1231219841.3455312$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$110891.584722$ |
| 15.1.717...984.1 |
$x^{15} - x - 2$ |
$15$ |
[1,7] |
$-\,2^{15}\cdot 17\cdot 12879212122287839$ |
$3$ |
$28.6452451595$ |
$2225802362.3038244$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$331366.035968$ |
| 15.1.717...151.1 |
$x^{15} - x - 4$ |
$15$ |
[1,7] |
$-\,349\cdot 20557173350492197499$ |
$2$ |
$28.6452481171$ |
$84702145777.55263$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$235580.127122$ |
| 15.1.753...288.1 |
$x^{15} + 2 x - 2$ |
$15$ |
[1,7] |
$-\,2^{14}\cdot 415522027\cdot 1107324941$ |
$3$ |
$28.739945361$ |
$1295376146.9074893$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$238966.641308$ |
| 15.1.790...576.1 |
$x^{15} + 4 x - 4$ |
$15$ |
[1,7] |
$-\,2^{14}\cdot 802609\cdot 600967491871$ |
$3$ |
$28.8304660568$ |
$1326291029.1877432$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$219984.816031$ |
| 15.5.836...871.1 |
$x^{15} - x^{14} - x^{13} - x^{12} - x^{11} + 6 x^{10} - 3 x^{9} + 5 x^{8} - 8 x^{7} + 4 x^{6} - x^{5} + x^{4} + x^{3} - 2 x^{2} + 3 x - 1$ |
$15$ |
[5,5] |
$-\,61\cdot 443437\cdot 309247046331703$ |
$3$ |
$28.9399530034$ |
$91460518976.96445$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$9$ |
$424231.084588$ |
| 15.7.133...872.1 |
$x^{15} - 2 x^{14} - 12 x^{13} + 21 x^{12} + 59 x^{11} - 84 x^{10} - 150 x^{9} + 160 x^{8} + 204 x^{7} - 150 x^{6} - 140 x^{5} + 67 x^{4} + 44 x^{3} - 13 x^{2} - 4 x + 1$ |
$15$ |
[7,4] |
$2^{3}\cdot 4373\cdot 411967\cdot 924989228549$ |
$4$ |
$29.8532238808$ |
$115460726104.23566$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$10$ |
$625563.074557$ |
| 15.5.136...456.1 |
$x^{15} - x^{14} - 6 x^{13} + 5 x^{12} + 13 x^{11} - 8 x^{10} - 15 x^{9} + 11 x^{8} + 7 x^{7} - 16 x^{6} - x^{5} + 17 x^{4} + 2 x^{3} - 7 x^{2} - x + 1$ |
$15$ |
[5,5] |
$-\,2^{3}\cdot 1999922317\cdot 853738824721$ |
$3$ |
$29.9016538528$ |
$116872967907.85727$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$9$ |
$474668.432119$ |
| 15.1.286...744.1 |
$x^{15} - 4 x - 8$ |
$15$ |
[1,7] |
$-\,2^{16}\cdot 11\cdot 39808288862597089$ |
$3$ |
$31.4188107079$ |
|
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$626759.530336$ |
| 15.1.540...224.1 |
$x^{15} - 4 x - 6$ |
$15$ |
[1,7] |
$-\,2^{14}\cdot 71\cdot 661\cdot 70232636190181$ |
$4$ |
$32.771368779$ |
$3467054897.883511$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$981286.864073$ |
| 15.1.114...024.1 |
$x^{15} + 4 x - 8$ |
$15$ |
[1,7] |
$-\,2^{18}\cdot 79\cdot 439\cdot 12626412250891$ |
$4$ |
$34.460964883$ |
|
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$993900.276319$ |
| 15.3.159...137.1 |
$x^{15} - 3 x - 1$ |
$15$ |
[3,6] |
$3^{15}\cdot 45736039\cdot 242958869$ |
$3$ |
$35.2241624334$ |
|
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$8$ |
$499991.418844$ |
| 15.1.159...887.1 |
$x^{15} + 3 x - 1$ |
$15$ |
[1,7] |
$-\,3^{16}\cdot 41\cdot 89\cdot 1015076033903$ |
$4$ |
$35.2241753319$ |
$454040984.9498909$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$672183.078836$ |
| 15.1.166...512.1 |
$x^{15} + 3 x - 2$ |
$15$ |
[1,7] |
$-\,2^{15}\cdot 3^{16}\cdot 118123441829$ |
$3$ |
$35.3276763948$ |
$12196757.103289274$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$1707481.62582$ |
| 15.7.307...424.1 |
$x^{15} - x^{14} - 11 x^{13} + 8 x^{12} + 48 x^{11} - 21 x^{10} - 108 x^{9} + 17 x^{8} + 137 x^{7} + 6 x^{6} - 99 x^{5} - 8 x^{4} + 38 x^{3} - 6 x + 1$ |
$15$ |
[7,4] |
$2^{11}\cdot 11\cdot 13667278608949991783$ |
$3$ |
$36.8038833618$ |
$82484026761.95607$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$10$ |
$3782469.74424$ |
| 15.9.893...832.1 |
$x^{15} - x^{14} - 10 x^{13} + 6 x^{12} + 38 x^{11} - 6 x^{10} - 67 x^{9} - 25 x^{8} + 52 x^{7} + 62 x^{6} - 10 x^{5} - 46 x^{4} - 5 x^{3} + 13 x^{2} + x - 1$ |
$15$ |
[9,3] |
$-\,2^{14}\cdot 83\cdot 181\cdot 10301\cdot 53681\cdot 6565421$ |
$6$ |
$39.5132371854$ |
$28044154922.746494$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$11$ |
$9166344.42892$ |
| 15.1.161...839.1 |
$x^{15} - 9 x - 9$ |
$15$ |
[1,7] |
$-\,3^{16}\cdot 67\cdot 257\cdot 2180316504061$ |
$4$ |
$41.1053013321$ |
$720199947.61693$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$1117243.81194$ |
| 15.1.193...863.1 |
$x^{15} - 3 x - 3$ |
$15$ |
[1,7] |
$-\,3^{15}\cdot 11\cdot 19\cdot 3246601\cdot 198739501$ |
$5$ |
$41.6017769647$ |
$1226266891.2787826$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$2849805.75625$ |
| 15.1.209...087.1 |
$x^{15} - 2 x - 3$ |
$15$ |
[1,7] |
$-\,19\cdot 739\cdot 317189\cdot 470191513156163$ |
$4$ |
$41.8214798471$ |
$1447089763885.2224$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$4523591.62487$ |
| 15.1.209...359.1 |
$x^{15} - x - 3$ |
$15$ |
[1,7] |
$-\,11\cdot 53\cdot 3592509248488922398673$ |
$3$ |
$41.8219645896$ |
$1447215565100.4592$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$3908642.03295$ |
| 15.1.209...391.1 |
$x^{15} + x - 3$ |
$15$ |
[1,7] |
$-\,5636003\cdot 371616713847216797$ |
$2$ |
$41.8219646192$ |
$1447215572778.6567$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$1864577.45524$ |
| 15.1.225...887.1 |
$x^{15} + 3 x - 3$ |
$15$ |
[1,7] |
$-\,3^{15}\cdot 23\cdot 4003\cdot 314407\cdot 5426327$ |
$5$ |
$42.0270294509$ |
$1323460854.461944$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$1667529.9049$ |
| 15.1.257...911.1 |
$x^{15} + 9 x - 9$ |
$15$ |
[1,7] |
$-\,3^{16}\cdot 136904431\cdot 436559161$ |
$3$ |
$42.3994326933$ |
$908698176.7657865$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$2184986.24273$ |
| 15.1.322...607.1 |
$x^{15} + 7 x - 4$ |
$15$ |
[1,7] |
$-\,1281803\cdot 2517610123640824469$ |
$2$ |
$43.0447956764$ |
$1796407584406.4954$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$6091177.35216$ |
| 15.1.470...875.1 |
$x^{15} - 5 x - 8$ |
$15$ |
[1,7] |
$-\,5^{13}\cdot 11\cdot 157\cdot 8231\cdot 270917639$ |
$5$ |
$44.1380170929$ |
$449287376.00423056$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$9653618.50754$ |
| 15.1.505...247.1 |
$x^{15} + 2 x - 5$ |
$15$ |
[1,7] |
$-\,13\cdot 388642222793347688836019$ |
$2$ |
$44.3506057177$ |
$2247743067237.339$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$7882405.8383$ |
| 15.3.119...184.1 |
$x^{15} - 4 x - 2$ |
$15$ |
[3,6] |
$2^{14}\cdot 289397\cdot 2514879509564333$ |
$3$ |
$46.9636752662$ |
$51518941661.36695$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$8$ |
$8430629.64598$ |
| 15.3.119...809.1 |
$x^{15} - 4 x - 1$ |
$15$ |
[3,6] |
$317\cdot 63716613109\cdot 590718277553$ |
$3$ |
$46.9655583953$ |
$3454189635686.093$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$8$ |
$12523127.2335$ |
