Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
23.1.831...703.1 |
x23 - 2x22 - 3x21 + 13x20 - 19x19 + 21x18 - 75x16 + 202x15 - 378x14 + 596x13 - 798x12 + 955x11 - 995x10 + 849x9 - 610x8 + 384x7 - 151x6 + 2x5 + 46x4 - 37x3 + 3x2 + 20x + 1 |
$23$ |
[1,11] |
$-\,647^{11}$ |
$1$ |
$22.0976212489$ |
|
|
|
$D_{23}$ (as 23T2) |
trivial |
$2$ |
$11$ |
$1561186.27544$ |
23.1.205...983.1 |
x23 - x - 1 |
$23$ |
[1,11] |
$-\,29\cdot 53264767\cdot 13296646221023838475181$ |
$3$ |
$22.9835192023$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$11$ |
$2560615.38998$ |
23.3.121...973.1 |
x23 - 3x21 - 6x20 + x19 + 17x18 + 18x17 - 10x16 - 43x15 - 25x14 + 33x13 + 60x12 + 11x11 - 54x10 - 47x9 + 12x8 + 44x7 + 15x6 - 17x5 - 16x4 + 6x2 + x - 1 |
$23$ |
[3,10] |
$7\cdot 41\cdot 599\cdot 7069315563547560848845133621$ |
$4$ |
$27.445087043$ |
|
|
not computed |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$53774282.4892$ |
23.1.152...439.1 |
x23 + 4x21 - 14x20 + 25x19 - 6x18 - 14x17 - 26x16 + 31x15 + 48x14 - 62x13 + 19x12 + 19x11 + 24x10 - 17x9 + 34x8 + 40x7 - 228x6 + 76x5 + 4x4 + 28x3 + 45x2 + 49x + 1 |
$23$ |
[1,11] |
$-\,1039^{11}$ |
$1$ |
$27.7159120747$ |
|
|
|
$D_{23}$ (as 23T2) |
trivial |
$2$ |
$11$ |
$55921894.4803$ |
23.1.293...047.1 |
x23 + 5x21 - 17x20 + 33x19 - 14x18 + 53x17 - 34x16 - 19x15 + 140x14 - 19x13 + 257x12 - 106x11 - 16x10 + 274x9 + 165x8 + 515x7 - 28x6 + 129x5 + 89x4 + 524x3 + 244x2 + 50x - 1 |
$23$ |
[1,11] |
$-\,1103^{11}$ |
$1$ |
$28.5196906393$ |
|
|
|
$D_{23}$ (as 23T2) |
trivial |
$2$ |
$11$ |
$42306743.1121$ |
23.7.484...792.1 |
x23 - 3x21 - 6x20 + x19 + 17x18 + 18x17 - 10x16 - 43x15 - 25x14 + 33x13 + 60x12 + 11x11 - 54x10 - 48x9 + 12x8 + 44x7 + 17x6 - 17x5 - 16x4 + 6x2 + x - 1 |
$23$ |
[7,8] |
$2^{3}\cdot 3^{2}\cdot 4231\cdot 4210631\cdot 3775042239237949162501$ |
$5$ |
$29.1452075964$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$14$ |
$179256140.602$ |
23.1.149...079.1 |
x23 - 7x22 + 15x21 - 6x20 + x19 - 21x18 + 17x17 + 2x16 + 46x15 - 10x14 + 108x13 - 129x12 - 98x11 - 144x10 - 85x9 + 8x8 + 187x7 - 82x6 + 363x5 + 216x4 - 128x3 - 51x2 + 77x - 1 |
$23$ |
[1,11] |
$-\,1279^{11}$ |
$1$ |
$30.612204664$ |
|
|
|
$D_{23}$ (as 23T2) |
trivial |
$2$ |
$11$ |
$195904703.063$ |
23.1.582...903.1 |
x23 - 2x22 + 16x21 - 34x20 + 68x19 - 63x18 + 17x17 + 43x16 - 139x15 + 165x14 + 25x13 - 228x12 + 265x11 - 270x10 + 75x9 + 246x8 - 130x7 - 161x6 + 240x5 - 393x4 + 569x3 - 385x2 + 99x + 1 |
$23$ |
[1,11] |
$-\,1447^{11}$ |
$1$ |
$32.4734497852$ |
|
|
|
$D_{23}$ (as 23T2) |
trivial |
$2$ |
$11$ |
$530761705.173$ |
23.1.697...671.1 |
x23 - 5x22 + 3x21 + 3x20 + 43x19 - 6x18 - 31x17 - 56x16 - 68x15 - 89x14 + 147x13 + 180x12 + 274x11 + 240x10 - 211x9 - 521x8 - 383x7 - 275x6 + 291x5 + 249x4 + 358x3 - 9x2 + 107x + 1 |
$23$ |
[1,11] |
$-\,1471^{11}$ |
$1$ |
$32.7299386538$ |
|
|
|
$D_{23}$ (as 23T2) |
trivial |
$2$ |
$11$ |
$492297100.302$ |
23.3.961...453.1 |
x23 - x22 - x21 - x20 + x19 + 8x18 - 3x17 - 9x16 - 6x15 + 5x14 + 23x13 - x12 - 23x11 - 13x10 + 12x9 + 27x8 - 3x7 - 20x6 - 6x5 + 9x4 + 7x3 - 4x2 - 2x + 1 |
$23$ |
[3,10] |
$19\cdot 28201\cdot 55057\cdot 3258654194756619414566191$ |
$4$ |
$33.1890102516$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$177401273.772$ |
23.1.100...339.1 |
x23 - 3x21 - 6x20 + x19 + 17x18 + 18x17 - 10x16 - 43x15 - 25x14 + 33x13 + 60x12 + 11x11 - 54x10 - 47x9 + 12x8 + 46x7 + 17x6 - 17x5 - 16x4 + 6x2 + x - 1 |
$23$ |
[1,11] |
$-\,167\cdot 30727\cdot 499717\cdot 39149185505838967853863$ |
$4$ |
$33.2515830019$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$11$ |
$139979317.774$ |
23.1.459...108.1 |
x23 - 2x22 - x21 + 5x20 - x19 - 4x18 + 6x15 + 6x14 - 17x13 - 10x12 + 31x11 + 5x10 - 32x9 + 25x7 - 17x5 + 2x4 + 9x3 - 3x2 - 2x + 1 |
$23$ |
[1,11] |
$-\,2^{2}\cdot 1021\cdot 425123\cdot 264472629367076822658099919$ |
$4$ |
$35.5239226707$ |
|
|
not computed |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$11$ |
$583250036.6$ |
23.1.687...411.1 |
x23 - 3x22 + 7x21 - 8x20 - 11x19 + 19x18 + 160x17 + 291x16 + 464x15 - 35x14 - 648x13 - 1313x12 - 1101x11 - 240x10 + 1477x9 + 1043x8 + 863x7 - 10x6 - 264x5 - 712x4 - 80x3 - 2304x2 - 2048x - 1024 |
$23$ |
[1,11] |
$-\,1811^{11}$ |
$1$ |
$36.1522149922$ |
|
|
|
$D_{23}$ (as 23T2) |
trivial |
$2$ |
$11$ |
$9293967260.34$ |
23.5.137...908.1 |
x23 - 3x21 - 6x20 + x19 + 17x18 + 18x17 - 10x16 - 43x15 - 25x14 + 33x13 + 60x12 + 11x11 - 54x10 - 47x9 + 12x8 + 43x7 + 17x6 - 17x5 - 16x4 + 6x2 + x - 1 |
$23$ |
[5,9] |
$-\,2^{2}\cdot 641\cdot 31357146703\cdot 17127956171402395614949$ |
$4$ |
$37.2613971261$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$13$ |
$3910844212.61$ |
23.1.167...576.1 |
x23 - 4x - 4 |
$23$ |
[1,11] |
$-\,2^{22}\cdot 8623\cdot 10045730659\cdot 4597557191821267$ |
$4$ |
$37.5755650454$ |
|
|
not computed |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$11$ |
$1131394806.61$ |
23.1.182...779.1 |
x23 - 11x22 + 47x21 - 78x20 - 51x19 + 367x18 - 359x17 - 364x16 + 1182x15 - 712x14 - 1586x13 + 3310x12 - 393x11 - 5271x10 + 5059x9 + 3246x8 - 8091x7 - 125x6 + 10047x5 - 6818x4 - 2608x3 + 2872x2 + 1488x - 2176 |
$23$ |
[1,11] |
$-\,1979^{11}$ |
$1$ |
$37.7190748431$ |
|
|
|
$D_{23}$ (as 23T2) |
trivial |
$2$ |
$11$ |
$15406380217.0$ |
23.5.250...508.1 |
x23 - 3x21 - 6x20 + x19 + 17x18 + 18x17 - 10x16 - 43x15 - 25x14 + 33x13 + 60x12 + 10x11 - 54x10 - 47x9 + 12x8 + 44x7 + 17x6 - 17x5 - 16x4 + 6x2 + x - 1 |
$23$ |
[5,9] |
$-\,2^{2}\cdot 1307\cdot 1787\cdot 28687\cdot 512717\cdot 18216368638827725857$ |
$6$ |
$38.2421954608$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$13$ |
$3444212420.75$ |
23.1.286...639.1 |
x23 + 2x - 1 |
$23$ |
[1,11] |
$-\,127\cdot 5892521806212607\cdot 3827252586261454951$ |
$3$ |
$38.4668488198$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$11$ |
$1296440588.69$ |
23.23.611...809.1 |
x23 - x22 - 22x21 + 21x20 + 210x19 - 190x18 - 1140x17 + 969x16 + 3876x15 - 3060x14 - 8568x13 + 6188x12 + 12376x11 - 8008x10 - 11440x9 + 6435x8 + 6435x7 - 3003x6 - 2002x5 + 715x4 + 286x3 - 66x2 - 12x + 1 |
$23$ |
[23,0] |
$47^{22}$ |
$1$ |
$39.7555669319$ |
|
✓ |
✓ |
$C_{23}$ (as 23T1) |
trivial |
$2$ |
$22$ |
$68215743661.4$ |
23.1.103...168.1 |
x23 + 4x - 4 |
$23$ |
[1,11] |
$-\,2^{22}\cdot 127\cdot 121259\cdot 78283735681\cdot 2050329605299$ |
$5$ |
$40.6796380099$ |
|
|
not computed |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$11$ |
$3908153739.94$ |
23.1.761...080.1 |
x23 - 8x - 8 |
$23$ |
[1,11] |
$-\,2^{22}\cdot 3\cdot 5\cdot 557\cdot 2100359171059\cdot 1034221960670111$ |
$6$ |
$44.363145749$ |
|
|
not computed |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$11$ |
$16501892392.2$ |
23.1.847...296.1 |
x23 - 2x - 2 |
$23$ |
[1,11] |
$-\,2^{22}\cdot 3\cdot 5519\cdot 1219883568588480577372817507$ |
$4$ |
$44.5699078639$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$11$ |
$12211948562.3$ |
23.1.875...784.1 |
x23 - x - 2 |
$23$ |
[1,11] |
$-\,2^{23}\cdot 7\cdot 24177221\cdot 78687506363\cdot 783971054543$ |
$5$ |
$44.6343866189$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$11$ |
$17404788077.7$ |
23.1.875...047.1 |
x23 - x - 4 |
$23$ |
[1,11] |
$-\,7901\cdot 159683\cdot 69415968602603755097356934209$ |
$3$ |
$44.6343866265$ |
|
|
not computed |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$11$ |
$10664511959.7$ |
23.1.875...368.1 |
x23 - 2 |
$23$ |
[1,11] |
$-\,2^{22}\cdot 23^{23}$ |
$2$ |
$44.6343866265$ |
|
|
✓ |
$F_{23}$ (as 23T4) |
trivial |
$2$ |
$11$ |
$14787749883.9$ |
23.1.904...440.1 |
x23 + 2x - 2 |
$23$ |
[1,11] |
$-\,2^{22}\cdot 5\cdot 9629\cdot 78977\cdot 5671055267529396512759$ |
$5$ |
$44.6968791201$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$11$ |
$11760180370.2$ |
23.1.990...656.1 |
x23 + 8x - 8 |
$23$ |
[1,11] |
$-\,2^{22}\cdot 19\cdot 2617\cdot 310741\cdot 1528181322635255601073$ |
$5$ |
$44.8735986096$ |
|
|
not computed |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$11$ |
$13784529892.7$ |
23.1.332...679.1 |
x23 - 9x - 9 |
$23$ |
[1,11] |
$-\,3^{22}\cdot 103\cdot 409\cdot 136973\cdot 1835872831815206461$ |
$5$ |
$47.299523925$ |
|
|
not computed |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$11$ |
$12917754140.4$ |
23.7.437...528.1 |
x23 - 3x22 + 4x20 + 5x19 - 5x18 - 14x17 + 4x16 + 15x15 + 10x14 - 22x13 - 13x12 + 16x11 + 18x10 - 3x9 - 23x8 + x7 + 13x6 + 4x5 - 7x4 - 4x3 + 5x2 + x - 1 |
$23$ |
[7,8] |
$2^{4}\cdot 17\cdot 241\cdot 1709\cdot 3877\cdot 111868093\cdot 346250347\cdot 25983511363$ |
$8$ |
$47.8659710754$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$14$ |
$78508567076.1$ |
23.1.101...875.1 |
x23 + 23x21 + 230x19 + 1311x17 + 4692x15 + 10948x13 + 16744x11 + 16445x9 + 9867x7 + 3289x5 + 506x3 + 23x - 1 |
$23$ |
[1,11] |
$-\,5^{11}\cdot 23^{23}$ |
$2$ |
$49.6612718765$ |
|
|
✓ |
$F_{23}$ (as 23T4) |
trivial |
$2$ |
$11$ |
$53144954646.2$ |
23.1.140...512.1 |
x23 - 4x - 8 |
$23$ |
[1,11] |
$-\,2^{26}\cdot 25811015603927\cdot 808975051375354229$ |
$3$ |
$50.3526826419$ |
|
|
not computed |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$11$ |
$61444013102.3$ |
23.15.902...637.1 |
x23 - 6x22 - 5x21 + 86x20 - 45x19 - 531x18 + 490x17 + 1869x16 - 1929x15 - 4166x14 + 4062x13 + 6124x12 - 4949x11 - 5930x10 + 3501x9 + 3657x8 - 1386x7 - 1348x6 + 286x5 + 273x4 - 28x3 - 27x2 + x + 1 |
$23$ |
[15,4] |
$90\!\cdots\!37$ |
$1$ |
$54.5998428171$ |
|
|
not computed |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$18$ |
$1818525117070$ |
23.9.955...636.1 |
x23 - x22 - 4x21 - 3x20 + 10x19 + 17x18 - 2x17 - 26x16 - 21x15 + 15x14 + 19x13 - 7x12 - 18x11 + 15x10 + 35x9 - 33x7 - 24x6 + 12x5 + 16x4 + 3x3 - 5x2 - 2x + 1 |
$23$ |
[9,7] |
$-\,2^{2}\cdot 19\cdot 432841815513398891\cdot 290448827022730856621$ |
$4$ |
$54.7356280457$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$15$ |
$973481536934$ |
23.15.124...500.1 |
x23 - 2x22 - 20x21 + 36x20 + 175x19 - 273x18 - 876x17 + 1134x16 + 2749x15 - 2812x14 - 5571x13 + 4267x12 + 7255x11 - 3939x10 - 5887x9 + 2181x8 + 2825x7 - 734x6 - 749x5 + 154x4 + 99x3 - 19x2 - 5x + 1 |
$23$ |
[15,4] |
$2^{2}\cdot 5^{4}\cdot 7499\cdot 275729\cdot 49942556731\cdot 48034096151655703$ |
$6$ |
$55.3596471245$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$18$ |
$2323935089500$ |
23.1.224...224.1 |
x23 + 4x - 8 |
$23$ |
[1,11] |
$-\,2^{30}\cdot 3\cdot 929\cdot 623071\cdot 16280269\cdot 738591239095427$ |
$6$ |
$56.8035733437$ |
|
|
not computed |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$11$ |
$402011657995$ |
23.1.285...320.1 |
x23 + 8x - 4 |
$23$ |
[1,11] |
$-\,2^{22}\cdot 5\cdot 24986142523\cdot 54552257894632015274417$ |
$4$ |
$57.4067141285$ |
|
|
not computed |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$11$ |
$281108277991$ |
23.9.300...043.1 |
x23 - 2x22 - 4x21 + 6x20 + 10x19 - 7x18 - 14x17 + 11x16 + 12x15 - 31x14 - 36x13 + 41x12 + 89x11 + 5x10 - 105x9 - 65x8 + 56x7 + 68x6 - 7x5 - 34x4 - 4x3 + 9x2 + x - 1 |
$23$ |
[9,7] |
$-\,508621\cdot 158113511\cdot 1092887040821\cdot 341802543194293$ |
$4$ |
$57.5308249537$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$15$ |
$394956948058$ |
23.3.321...401.1 |
x23 - 3x - 1 |
$23$ |
[3,10] |
$259028266789\cdot 124091112112198565028075828709$ |
$2$ |
$57.7002549387$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$208932361073$ |
23.1.321...535.1 |
x23 + 3x - 1 |
$23$ |
[1,11] |
$-\,5\cdot 22723592653\cdot 282905139402414328282680249319$ |
$3$ |
$57.7002549419$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$11$ |
$185847611513$ |
23.1.322...336.1 |
x23 + 3x - 2 |
$23$ |
[1,11] |
$-\,2^{23}\cdot 17\cdot 43\cdot 67\cdot 971821\cdot 15873405731\cdot 5085469520371$ |
$7$ |
$57.7070814215$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$11$ |
$407641553662$ |
23.13.425...343.1 |
x23 - 7x22 + 2x21 + 88x20 - 150x19 - 422x18 + 1148x17 + 862x16 - 4167x15 - 105x14 + 8563x13 - 2935x12 - 10393x11 + 5920x10 + 7285x9 - 5405x8 - 2661x7 + 2503x6 + 356x5 - 537x4 + 19x3 + 39x2 - 2x - 1 |
$23$ |
[13,5] |
$-\,13\cdot 1289\cdot 4057217\cdot 26391289\cdot 32505503\cdot 7288751994309941$ |
$6$ |
$64.5556967352$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$17$ |
$4090939159600$ |
23.1.623...335.1 |
x23 - 3x - 3 |
$23$ |
[1,11] |
$-\,3^{22}\cdot 5\cdot 203008301\cdot 19561943299801571525063$ |
$4$ |
$65.6379381689$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$11$ |
$933328504105$ |
23.1.655...231.1 |
x23 - 2x - 3 |
$23$ |
[1,11] |
$-\,587\cdot 75967200927041\cdot 14694056584644694851886093$ |
$3$ |
$65.7816262406$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$11$ |
$951514783980$ |
23.1.655...719.1 |
x23 - x - 3 |
$23$ |
[1,11] |
$-\,41\cdot 263\cdot 455033\cdot 13\!\cdots\!21$ |
$4$ |
$65.781638742$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$11$ |
$1198293682960$ |
23.1.655...303.1 |
x23 - 3 |
$23$ |
[1,11] |
$-\,3^{22}\cdot 23^{23}$ |
$2$ |
$65.781638742$ |
|
|
✓ |
$F_{23}$ (as 23T4) |
trivial |
$2$ |
$11$ |
$1289649122770$ |
23.1.655...887.1 |
x23 + x - 3 |
$23$ |
[1,11] |
$-\,859\cdot 1733\cdot 44\!\cdots\!21$ |
$3$ |
$65.781638742$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$11$ |
$813269772507$ |
23.1.687...271.1 |
x23 + 3x - 3 |
$23$ |
[1,11] |
$-\,3^{22}\cdot 7\cdot 467399\cdot 10931299891\cdot 612464196024013$ |
$5$ |
$65.9187485478$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$11$ |
$993709440615$ |
23.17.696...863.1 |
x23 - 3x22 - 18x21 + 55x20 + 141x19 - 429x18 - 638x17 + 1858x16 + 1864x15 - 4889x14 - 3693x13 + 8033x12 + 4990x11 - 8160x10 - 4433x9 + 4919x8 + 2383x7 - 1652x6 - 677x5 + 297x4 + 89x3 - 27x2 - 4x + 1 |
$23$ |
[17,3] |
$-\,17\cdot 40\!\cdots\!39$ |
$2$ |
$65.9575950422$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$19$ |
$36539551739300$ |
23.1.751...207.1 |
x23 + 9x - 9 |
$23$ |
[1,11] |
$-\,3^{22}\cdot 151\cdot 158631250967721112920032141873$ |
$3$ |
$66.175479984$ |
|
|
not computed |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$11$ |
$640542907885$ |
23.11.110...432.1 |
x23 - 7x22 + 2x21 + 88x20 - 150x19 - 422x18 + 1148x17 + 862x16 - 4167x15 - 105x14 + 8563x13 - 2935x12 - 10393x11 + 5920x10 + 7285x9 - 5405x8 - 2661x7 + 2503x6 + 354x5 - 537x4 + 18x3 + 39x2 - 2x - 1 |
$23$ |
[11,6] |
$2^{10}\cdot 22483\cdot 2527336563667297\cdot 19007452217635529293$ |
$4$ |
$67.2959220635$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$16$ |
$11886760766000$ |