| 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 |
| 37.37.171...601.1 |
$x^{37} - x^{36} - 72 x^{35} + 67 x^{34} + 2278 x^{33} - 1964 x^{32} - 41849 x^{31} + 33262 x^{30} + 497142 x^{29} - 362207 x^{28} - 4027127 x^{27} + 2672215 x^{26} + 22871279 x^{25} - 13719683 x^{24} - 92273266 x^{23} + 49606380 x^{22} + 265291071 x^{21} - 126402144 x^{20} - 540999671 x^{19} + 224635365 x^{18} + 773506030 x^{17} - 271832880 x^{16} - 761221384 x^{15} + 214848879 x^{14} + 502240682 x^{13} - 103923082 x^{12} - 213804070 x^{11} + 27920639 x^{10} + 55105551 x^{9} - 3603129 x^{8} - 7708785 x^{7} + 235974 x^{6} + 497852 x^{5} - 22640 x^{4} - 12819 x^{3} + 1020 x^{2} + 28 x - 1$ |
$37$ |
[37,0] |
$149^{36}$ |
$1$ |
$130.15219727$ |
$130.15219726971506$ |
|
✓ |
|
$C_{37}$ (as 37T1) |
trivial |
$2$ |
$36$ |
$2217351755002491400000000000$ |
| 37.37.345...561.1 |
$x^{37} - x^{36} - 108 x^{35} + 245 x^{34} + 4913 x^{33} - 17429 x^{32} - 115073 x^{31} + 605121 x^{30} + 1258904 x^{29} - 11895493 x^{28} + 1401577 x^{27} + 136786740 x^{26} - 218698801 x^{25} - 851925353 x^{24} + 2810760540 x^{23} + 1559768964 x^{22} - 17408647490 x^{21} + 14765496491 x^{20} + 52555917850 x^{19} - 112901823056 x^{18} - 30825357400 x^{17} + 320568348295 x^{16} - 255996383256 x^{15} - 343575615312 x^{14} + 697695088122 x^{13} - 135330997139 x^{12} - 635742178755 x^{11} + 559084397332 x^{10} + 98854779029 x^{9} - 379266961937 x^{8} + 152281955055 x^{7} + 65816775545 x^{6} - 70480276872 x^{5} + 12914339542 x^{4} + 6483753572 x^{3} - 3469705332 x^{2} + 579396241 x - 30247313$ |
$37$ |
[37,0] |
$223^{36}$ |
$1$ |
$192.680233546$ |
$192.6802335458486$ |
|
✓ |
|
$C_{37}$ (as 37T1) |
trivial |
$2$ |
$36$ |
$2669696754256726600000000000000$ |
| 37.37.676...801.1 |
$x^{37} - x^{36} - 288 x^{35} + 203 x^{34} + 35910 x^{33} - 17336 x^{32} - 2554843 x^{31} + 842615 x^{30} + 115283443 x^{29} - 27504461 x^{28} - 3475263507 x^{27} + 687931612 x^{26} + 71915662407 x^{25} - 13974595438 x^{24} - 1034496050617 x^{23} + 221330910643 x^{22} + 10365088714029 x^{21} - 2534502436630 x^{20} - 71813314605418 x^{19} + 19740632343658 x^{18} + 338381715805464 x^{17} - 99305962871851 x^{16} - 1055972317034939 x^{15} + 302779333586209 x^{14} + 2104618406390649 x^{13} - 505910437546894 x^{12} - 2560928454934750 x^{11} + 376597618487442 x^{10} + 1787314591059035 x^{9} - 20429122626927 x^{8} - 643936928000107 x^{7} - 89391122404607 x^{6} + 89662863870162 x^{5} + 25891375086732 x^{4} + 1113091773432 x^{3} - 112807611860 x^{2} - 8478121776 x - 123515969$ |
$37$ |
[37,0] |
$593^{36}$ |
$1$ |
$499.007725404$ |
$499.007725403986$ |
|
✓ |
|
$C_{37}$ (as 37T1) |
not computed |
$2$ |
$36$ |
|
| 37.37.813...681.1 |
$x^{37} - 666 x^{35} - 481 x^{34} + 193399 x^{33} + 256521 x^{32} - 32436827 x^{31} - 60004084 x^{30} + 3503452596 x^{29} + 8113398850 x^{28} - 257000630926 x^{27} - 704292185114 x^{26} + 13150853376643 x^{25} + 41268101524916 x^{24} - 474337598223255 x^{23} - 1672482254287228 x^{22} + 12032466243732809 x^{21} + 47286637172470867 x^{20} - 211502629431882231 x^{19} - 929675982328753625 x^{18} + 2498958523266151636 x^{17} + 12536142236443615902 x^{16} - 18791897342800992970 x^{15} - 113239929214497210129 x^{14} + 80927529107744817385 x^{13} + 663966210336111429023 x^{12} - 146546651897009713442 x^{11} - 2439258160361411529393 x^{10} - 154326326264692800324 x^{9} + 5386184266991634344483 x^{8} + 1055793633392402952768 x^{7} - 6769150214799915444440 x^{6} - 1552196159553019851407 x^{5} + 4355671676506075568364 x^{4} + 921754431147330625307 x^{3} - 1108584774969076393499 x^{2} - 217498966742521653325 x + 51140551819476687829$ |
$37$ |
[37,0] |
$37^{72}$ |
$1$ |
$1126.25255021$ |
$1126.2525502057642$ |
|
✓ |
|
$C_{37}$ (as 37T1) |
not computed |
$2$ |
$36$ |
|
