| 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 |
| 37.1.771...893.1 |
$x^{37} - 13 x^{36} + 85 x^{35} - 385 x^{34} + 1376 x^{33} - 4093 x^{32} + 10351 x^{31} - 22625 x^{30} + 43550 x^{29} - 74960 x^{28} + 116443 x^{27} - 165086 x^{26} + 217576 x^{25} - 271252 x^{24} + 323555 x^{23} - 372277 x^{22} + 413102 x^{21} - 438049 x^{20} + 446097 x^{19} - 447021 x^{18} + 444655 x^{17} - 438731 x^{16} + 440293 x^{15} - 414266 x^{14} + 384032 x^{13} - 341418 x^{12} + 287526 x^{11} - 243684 x^{10} + 191804 x^{9} - 128361 x^{8} + 79830 x^{7} - 27930 x^{6} + 19250 x^{5} - 11450 x^{4} + 10067 x^{3} - 4360 x^{2} + 789 x - 52$ |
$37$ |
[1,18] |
$37^{35}$ |
$1$ |
$30.4392581136693$ |
$33.46883265603228$ |
|
|
? |
$F_{37}$ (as 37T9) |
trivial |
$2$ |
$18$ |
$11999819427965.701$ |
| 37.1.104...381.1 |
$x^{37} - x - 1$ |
$37$ |
[1,18] |
$983\cdot 10\!\cdots\!07$ |
$2$ |
$36.9898710435$ |
$1.0221911561373473e+29$ |
|
|
✓ |
$S_{37}$ (as 37T11) |
trivial |
$2$ |
$18$ |
$94459733489984.19$ |
| 37.1.106...653.1 |
$x^{37} + x - 1$ |
$37$ |
[1,18] |
$19\cdot 11323755688122007063\cdot 49\!\cdots\!49$ |
$3$ |
$37.0100301069$ |
$1.0325464790846705e+29$ |
|
|
✓ |
$S_{37}$ (as 37T11) |
trivial |
$2$ |
$18$ |
$232694775426930.7$ |
| 37.1.146...709.1 |
$x^{37} + 2 x - 1$ |
$37$ |
[1,18] |
$13\cdot 79\cdot 3203\cdot 230203\cdot 34944191\cdot 52002217\cdot 4124383231\cdot 25\!\cdots\!59$ |
$8$ |
$65.3537130156$ |
$3.823841953282166e+33$ |
|
|
✓ |
$S_{37}$ (as 37T11) |
trivial |
$2$ |
$18$ |
$9551296549801247000$ |
| 37.1.696...128.1 |
$x^{37} - 4 x - 4$ |
$37$ |
[1,18] |
$2^{36}\cdot 233\cdot 373\cdot 78191\cdot 71872279\cdot 16291354255739\cdot 1273067852382060949050712307$ |
$7$ |
$72.5458784279$ |
$1.975558468319023e+29$ |
|
|
? |
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$18$ |
|
| 37.1.710...320.1 |
$x^{37} - 2 x - 2$ |
$37$ |
[1,18] |
$2^{36}\cdot 5\cdot 7\cdot 151\cdot 9239\cdot 119446257446842253309\cdot 17\!\cdots\!07$ |
$7$ |
$72.5866483199$ |
$1.9961992138047286e+29$ |
|
|
✓ |
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$18$ |
|
| 37.1.725...376.1 |
$x^{37} - x - 2$ |
$37$ |
[1,18] |
$2^{36}\cdot 255111423183900271\cdot 31886261543528230373\cdot 1297568460899930754527$ |
$4$ |
$72.6266101467$ |
|
|
|
✓ |
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$18$ |
|
| 37.1.725...736.1 |
$x^{37} - x - 4$ |
$37$ |
[1,18] |
$2^{38}\cdot 40158589\cdot 859997730921167\cdot 76\!\cdots\!63$ |
$4$ |
$72.6266101467$ |
|
|
|
? |
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$18$ |
|
| 37.1.725...512.1 |
$x^{37} - 2$ |
$37$ |
[1,18] |
$2^{36}\cdot 37^{37}$ |
$2$ |
$72.6266101467$ |
$79.85502972178021$ |
|
|
✓ |
$F_{37}$ (as 37T9) |
not computed |
$2$ |
$18$ |
|
| 37.1.739...704.1 |
$x^{37} + 2 x - 2$ |
$37$ |
[1,18] |
$2^{36}\cdot 11\cdot 13\cdot 29\cdot 8111\cdot 32\!\cdots\!17$ |
$6$ |
$72.6657957379$ |
$2.0368533035272427e+29$ |
|
|
✓ |
$S_{37}$ (as 37T11) |
trivial |
$2$ |
$18$ |
$109736008063969670000$ |
| 37.1.754...896.1 |
$x^{37} + 4 x - 4$ |
$37$ |
[1,18] |
$2^{36}\cdot 41\cdot 11851181\cdot 1770736411\cdot 12\!\cdots\!31$ |
$5$ |
$72.7042350707$ |
$2.056879048349089e+29$ |
|
|
? |
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$18$ |
|
| 37.3.479...851.1 |
$x^{37} - 3 x - 1$ |
$37$ |
[3,17] |
$-\,11\cdot 103\cdot 13781\cdot 868727\cdot 1508693\cdot 35096465749296997\cdot 66\!\cdots\!61$ |
$7$ |
$98.0305695216$ |
$6.921308800624237e+36$ |
|
|
✓ |
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$19$ |
|
| 37.1.479...885.1 |
$x^{37} + 3 x - 1$ |
$37$ |
[1,18] |
$5\cdot 17\cdot 23\cdot 503\cdot 8237\cdot 17707\cdot 6366766785751\cdot 52\!\cdots\!61$ |
$8$ |
$98.0305695216$ |
$6.921308800624239e+36$ |
|
|
✓ |
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$18$ |
|
| 37.1.652...077.1 |
$x^{37} + 3 x - 3$ |
$37$ |
[1,18] |
$3^{36}\cdot 211\cdot 6139531\cdot 8271665508919\cdot 6321124050660239\cdot 6421792279973985077$ |
$6$ |
$98.8542412001$ |
$6.073746714558556e+28$ |
|
|
? |
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$18$ |
|
| 37.1.153...189.1 |
$x^{37} - 3 x - 3$ |
$37$ |
[1,18] |
$3^{36}\cdot 9598397\cdot 10\!\cdots\!97$ |
$3$ |
$107.663232105$ |
$2.946392829551214e+29$ |
|
|
✓ |
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$18$ |
|
| 37.1.158...365.1 |
$x^{37} - 2 x - 3$ |
$37$ |
[1,18] |
$3^{36}\cdot 5\cdot 7\cdot 1493\cdot 137771\cdot 867792304013\cdot 16\!\cdots\!81$ |
$7$ |
$107.75261276$ |
|
|
|
✓ |
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$18$ |
|
| 37.1.158...421.1 |
$x^{37} - x - 3$ |
$37$ |
[1,18] |
$3^{36}\cdot 10\!\cdots\!01$ |
$2$ |
$107.752612787$ |
|
|
|
✓ |
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$18$ |
|
| 37.1.158...557.1 |
$x^{37} - 3$ |
$37$ |
[1,18] |
$3^{36}\cdot 37^{37}$ |
$2$ |
$107.752612787$ |
$118.47707168667975$ |
|
|
✓ |
$F_{37}$ (as 37T9) |
not computed |
$2$ |
$18$ |
|
| 37.1.158...693.1 |
$x^{37} + x - 3$ |
$37$ |
[1,18] |
$3^{36}\cdot 19\cdot 349\cdot 4501649\cdot 1182640248703\cdot 29\!\cdots\!69$ |
$6$ |
$107.752612787$ |
|
|
|
✓ |
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$18$ |
|
| 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 |
$2$ |
$36$ |
$2217351755002491400000000000$ |
| 37.3.200...112.1 |
$x^{37} - 4 x - 2$ |
$37$ |
[3,17] |
$-\,2^{36}\cdot 1181\cdot 156768103\cdot 3595021207\cdot 43\!\cdots\!67$ |
$5$ |
$130.707426027$ |
$1.0614730718773003e+34$ |
|
|
✓ |
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$19$ |
|
| 37.3.200...107.1 |
$x^{37} - 4 x - 1$ |
$37$ |
[3,17] |
$-\,53\cdot 139\cdot 27\!\cdots\!21$ |
$3$ |
$130.707426029$ |
$1.4176037499701838e+39$ |
|
|
✓ |
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$19$ |
|
| 37.1.200...136.1 |
$x^{37} + 4 x - 2$ |
$37$ |
[1,18] |
$2^{36}\cdot 249494962454898495919\cdot 11\!\cdots\!79$ |
$3$ |
$130.70742603$ |
$1.0614730722604274e+34$ |
|
|
✓ |
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$18$ |
|
| 37.1.201...181.1 |
$x^{37} + 4 x - 3$ |
$37$ |
[1,18] |
$3^{36}\cdot 839348831\cdot 15\!\cdots\!31$ |
$3$ |
$130.710209914$ |
|
|
|
✓ |
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$18$ |
|
| 37.1.124...160.1 |
$x^{37} - 2 x - 4$ |
$37$ |
[1,18] |
$2^{70}\cdot 5\cdot 7\cdot 47\cdot 64\!\cdots\!17$ |
$5$ |
$137.314984457$ |
|
|
|
? |
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$18$ |
|
| 37.1.124...256.1 |
$x^{37} + 2 x - 4$ |
$37$ |
[1,18] |
$2^{70}\cdot 13\cdot 137\cdot 195791\cdot 10489284688357\cdot 5723750340436657\cdot 504174169295944373011$ |
$7$ |
$137.314984457$ |
|
|
|
? |
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$18$ |
|
| 37.1.498...464.1 |
$x^{37} - 3 x - 4$ |
$37$ |
[1,18] |
$2^{73}\cdot 9739\cdot 174331\cdot 36662321\cdot 289516438999\cdot 95795519149931\cdot 3057074418307037$ |
$7$ |
$142.557415254$ |
|
|
|
✓ |
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$18$ |
|
| 37.1.498...968.1 |
$x^{37} + x - 4$ |
$37$ |
[1,18] |
$2^{73}\cdot 19\cdot 311\cdot 20831443951883\cdot 42\!\cdots\!57$ |
$5$ |
$142.557418957$ |
|
|
|
✓ |
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$18$ |
|
| 37.1.860...173.1 |
$x^{37} + 5 x - 3$ |
$37$ |
[1,18] |
$3^{34}\cdot 7\cdot 17\cdot 439\cdot 4064647\cdot 22665391718591\cdot 10\!\cdots\!81$ |
$7$ |
$153.964267333$ |
|
|
|
|
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$18$ |
|
| 37.1.193...128.1 |
$x^{37} + 5 x - 2$ |
$37$ |
[1,18] |
$2^{34}\cdot 7\cdot 8599\cdot 1088665069\cdot 284461581404201\cdot 60\!\cdots\!01$ |
$6$ |
$157.375956868$ |
|
|
|
|
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$18$ |
|
| 37.3.774...443.1 |
$x^{37} - 5 x - 3$ |
$37$ |
[3,17] |
$-\,3^{36}\cdot 43\cdot 1907\cdot 62\!\cdots\!83$ |
$4$ |
$163.384281632$ |
|
|
|
✓ |
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$19$ |
|
| 37.1.774...517.1 |
$x^{37} + 5 x - 1$ |
$37$ |
[1,18] |
$7\cdot 47\cdot 23\!\cdots\!73$ |
$3$ |
$163.384282536$ |
$8.798124312680973e+40$ |
|
|
✓ |
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$18$ |
|
| 37.1.779...832.1 |
$x^{37} + 5 x - 4$ |
$37$ |
[1,18] |
$2^{73}\cdot 7\cdot 37573\cdot 161999\cdot 10047643\cdot 4972224617011\cdot 387504669093621087013178459593$ |
$7$ |
$163.412628743$ |
|
|
|
✓ |
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$18$ |
|
| 37.1.145...125.1 |
$x^{37} - 5 x - 5$ |
$37$ |
[1,18] |
$5^{36}\cdot 563\cdot 175944697081\cdot 746724389353\cdot 13\!\cdots\!43$ |
$5$ |
$176.877946858$ |
$4.792720264945012e+29$ |
|
|
✓ |
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$18$ |
|
| 37.1.153...501.1 |
$x^{37} - 4 x - 5$ |
$37$ |
[1,18] |
$15\!\cdots\!01$ |
$1$ |
$177.125257097$ |
$3.919125151102706e+41$ |
|
|
✓ |
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$18$ |
|
| 37.1.153...757.1 |
$x^{37} - 3 x - 5$ |
$37$ |
[1,18] |
$47\cdot 4458653\cdot 39030547\cdot 4191145897\cdot 2748399402101\cdot 46040166590110289\cdot 35410190689086361595487217777$ |
$7$ |
$177.125319729$ |
$3.91915078878761e+41$ |
|
|
✓ |
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$18$ |
|
| 37.1.153...933.1 |
$x^{37} - 2 x - 5$ |
$37$ |
[1,18] |
$7\cdot 34591\cdot 96167\cdot 163386011\cdot 40\!\cdots\!57$ |
$5$ |
$177.12531973$ |
$3.9191507893987696e+41$ |
|
|
✓ |
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$18$ |
|
| 37.1.153...989.1 |
$x^{37} - x - 5$ |
$37$ |
[1,18] |
$11\cdot 107\cdot 359\cdot 60013\cdot 22231407377\cdot 27\!\cdots\!23$ |
$6$ |
$177.12531973$ |
$3.9191507893987696e+41$ |
|
|
✓ |
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$18$ |
|
| 37.1.153...125.1 |
$x^{37} - 5$ |
$37$ |
[1,18] |
$5^{36}\cdot 37^{37}$ |
$2$ |
$177.12531973$ |
$194.75434201004887$ |
|
|
✓ |
$F_{37}$ (as 37T9) |
not computed |
$2$ |
$18$ |
|
| 37.1.161...125.1 |
$x^{37} + 5 x - 5$ |
$37$ |
[1,18] |
$5^{36}\cdot 7\cdot 17\cdot 39619\cdot 50081864423\cdot 2601293855703705209\cdot 18050801224775844479711$ |
$7$ |
$177.360848235$ |
$5.040659391404967e+29$ |
|
|
✓ |
$S_{37}$ (as 37T11) |
not computed |
$2$ |
$18$ |
|
| 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 |
$2$ |
$36$ |
|
