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Label Polynomial Discriminant Galois group Class group
23.1.8316624386164136054632388935703.1 x23 - 2x22 - 3x21 + 13x20 - 19x19 + 21x18 - 75x16 + 202x15 - 378x14 + 596x13 - 798x12 + 955x11 - 995x10 + 849x9 - 610x8 + 384x7 - 151x6 + 2x5 + 46x4 - 37x3 + 3x2 + 20x + 1 \( -\,647^{11} \) $D_{23}$ (as 23T2) Trivial (GRH)
23.1.20539040122483692476958386186983.1 x23 - x - 1 \( -\,29\cdot 53264767\cdot 13296646221023838475181 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.3.1215307246476151828207513456186973.1 x23 - 3x21 - 6x20 + x19 + 17x18 + 18x17 - 10x16 - 43x15 - 25x14 + 33x13 + 60x12 + 11x11 - 54x10 - 47x9 + 12x8 + 44x7 + 15x6 - 17x5 - 16x4 + 6x2 + x - 1 \( 7\cdot 41\cdot 599\cdot 7069315563547560848845133621 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.1.1523249425950439235855871175083439.1 x23 + 4x21 - 14x20 + 25x19 - 6x18 - 14x17 - 26x16 + 31x15 + 48x14 - 62x13 + 19x12 + 19x11 + 24x10 - 17x9 + 34x8 + 40x7 - 228x6 + 76x5 + 4x4 + 28x3 + 45x2 + 49x + 1 \( -\,1039^{11} \) $D_{23}$ (as 23T2) Trivial (GRH)
23.1.2939886993377131174870795633320047.1 x23 + 5x21 - 17x20 + 33x19 - 14x18 + 53x17 - 34x16 - 19x15 + 140x14 - 19x13 + 257x12 - 106x11 - 16x10 + 274x9 + 165x8 + 515x7 - 28x6 + 129x5 + 89x4 + 524x3 + 244x2 + 50x - 1 \( -\,1103^{11} \) $D_{23}$ (as 23T2) Trivial (GRH)
23.7.4842220039012226302771299504642792.1 x23 - 3x21 - 6x20 + x19 + 17x18 + 18x17 - 10x16 - 43x15 - 25x14 + 33x13 + 60x12 + 11x11 - 54x10 - 48x9 + 12x8 + 44x7 + 17x6 - 17x5 - 16x4 + 6x2 + x - 1 \( 2^{3}\cdot 3^{2}\cdot 4231\cdot 4210631\cdot 3775042239237949162501 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.1.14982213765271379362645677088782079.1 x23 - 7x22 + 15x21 - 6x20 + x19 - 21x18 + 17x17 + 2x16 + 46x15 - 10x14 + 108x13 - 129x12 - 98x11 - 144x10 - 85x9 + 8x8 + 187x7 - 82x6 + 363x5 + 216x4 - 128x3 - 51x2 + 77x - 1 \( -\,1279^{11} \) $D_{23}$ (as 23T2) Trivial (GRH)
23.1.58230945563524325903440619509366903.1 x23 - 2x22 + 16x21 - 34x20 + 68x19 - 63x18 + 17x17 + 43x16 - 139x15 + 165x14 + 25x13 - 228x12 + 265x11 - 270x10 + 75x9 + 246x8 - 130x7 - 161x6 + 240x5 - 393x4 + 569x3 - 385x2 + 99x + 1 \( -\,1447^{11} \) $D_{23}$ (as 23T2) Trivial (GRH)
23.1.69781355284066743169711357773860671.1 x23 - 5x22 + 3x21 + 3x20 + 43x19 - 6x18 - 31x17 - 56x16 - 68x15 - 89x14 + 147x13 + 180x12 + 274x11 + 240x10 - 211x9 - 521x8 - 383x7 - 275x6 + 291x5 + 249x4 + 358x3 - 9x2 + 107x + 1 \( -\,1471^{11} \) $D_{23}$ (as 23T2) Trivial (GRH)
23.3.96132210542339215127450630436634453.1 x23 - x22 - x21 - x20 + x19 + 8x18 - 3x17 - 9x16 - 6x15 + 5x14 + 23x13 - x12 - 23x11 - 13x10 + 12x9 + 27x8 - 3x7 - 20x6 - 6x5 + 9x4 + 7x3 - 4x2 - 2x + 1 \( 19\cdot 28201\cdot 55057\cdot 3258654194756619414566191 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.1.100388389417020021246100166894420339.1 x23 - 3x21 - 6x20 + x19 + 17x18 + 18x17 - 10x16 - 43x15 - 25x14 + 33x13 + 60x12 + 11x11 - 54x10 - 47x9 + 12x8 + 46x7 + 17x6 - 17x5 - 16x4 + 6x2 + x - 1 \( -\,167\cdot 30727\cdot 499717\cdot 39149185505838967853863 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.1.459177995857290463522143518056811108.1 x23 - 2x22 - x21 + 5x20 - x19 - 4x18 + 6x15 + 6x14 - 17x13 - 10x12 + 31x11 + 5x10 - 32x9 + 25x7 - 17x5 + 2x4 + 9x3 - 3x2 - 2x + 1 \( -\,2^{2}\cdot 1021\cdot 425123\cdot 264472629367076822658099919 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.1.687231335140465279781021461534970411.1 x23 - 3x22 + 7x21 - 8x20 - 11x19 + 19x18 + 160x17 + 291x16 + 464x15 - 35x14 - 648x13 - 1313x12 - 1101x11 - 240x10 + 1477x9 + 1043x8 + 863x7 - 10x6 - 264x5 - 712x4 - 80x3 - 2304x2 - 2048x - 1024 \( -\,1811^{11} \) $D_{23}$ (as 23T2) Trivial (GRH)
23.5.1377082951373957855841789612501108908.1 x23 - 3x21 - 6x20 + x19 + 17x18 + 18x17 - 10x16 - 43x15 - 25x14 + 33x13 + 60x12 + 11x11 - 54x10 - 47x9 + 12x8 + 43x7 + 17x6 - 17x5 - 16x4 + 6x2 + x - 1 \( -\,2^{2}\cdot 641\cdot 31357146703\cdot 17127956171402395614949 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.1.1670424922585164788805622697952280576.1 x23 - 4x - 4 \( -\,2^{22}\cdot 8623\cdot 10045730659\cdot 4597557191821267 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.1.1823491470737247969166873376199879779.1 x23 - 11x22 + 47x21 - 78x20 - 51x19 + 367x18 - 359x17 - 364x16 + 1182x15 - 712x14 - 1586x13 + 3310x12 - 393x11 - 5271x10 + 5059x9 + 3246x8 - 8091x7 - 125x6 + 10047x5 - 6818x4 - 2608x3 + 2872x2 + 1488x - 2176 \( -\,1979^{11} \) $D_{23}$ (as 23T2) Trivial (GRH)
23.5.2503137973364726455090108816728094508.1 x23 - 3x21 - 6x20 + x19 + 17x18 + 18x17 - 10x16 - 43x15 - 25x14 + 33x13 + 60x12 + 10x11 - 54x10 - 47x9 + 12x8 + 44x7 + 17x6 - 17x5 - 16x4 + 6x2 + x - 1 \( -\,2^{2}\cdot 1307\cdot 1787\cdot 28687\cdot 512717\cdot 18216368638827725857 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.1.2864125503948510940846004233663441639.1 x23 + 2x - 1 \( -\,127\cdot 5892521806212607\cdot 3827252586261454951 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.23.6111571184724799803076702357055363809.1 x23 - x22 - 22x21 + 21x20 + 210x19 - 190x18 - 1140x17 + 969x16 + 3876x15 - 3060x14 - 8568x13 + 6188x12 + 12376x11 - 8008x10 - 11440x9 + 6435x8 + 6435x7 - 3003x6 - 2002x5 + 715x4 + 286x3 - 66x2 - 12x + 1 \( 47^{22} \) $C_{23}$ (as 23T1) Trivial (GRH)
23.1.10367471077843902113690154634909319168.1 x23 + 4x - 4 \( -\,2^{22}\cdot 127\cdot 121259\cdot 78283735681\cdot 2050329605299 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.1.76122611959712052465607572442400686080.1 x23 - 8x - 8 \( -\,2^{22}\cdot 3\cdot 5\cdot 557\cdot 2100359171059\cdot 1034221960670111 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.1.84714925830153585744409482078292279296.1 x23 - 2x - 2 \( -\,2^{22}\cdot 3\cdot 5519\cdot 1219883568588480577372817507 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.1.87579030112206219473123894560276086784.1 x23 - x - 2 \( -\,2^{23}\cdot 7\cdot 24177221\cdot 78687506363\cdot 783971054543 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.1.87579030453634015434594065117161697047.1 x23 - x - 4 \( -\,7901\cdot 159683\cdot 69415968602603755097356934209 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.1.87579030453634096837343451956922810368.1 x23 - 2 \( -\,2^{22}\cdot 23^{23} \) $F_{23}$ (as 23T4) Trivial (GRH)
23.1.90443135077114607930277421835553341440.1 x23 + 2x - 2 \( -\,2^{22}\cdot 5\cdot 9629\cdot 78977\cdot 5671055267529396512759 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.1.99035448947556141209079331471444934656.1 x23 + 8x - 8 \( -\,2^{22}\cdot 19\cdot 2617\cdot 310741\cdot 1528181322635255601073 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.1.332434202154298684636783958613993659679.1 x23 - 9x - 9 \( -\,3^{22}\cdot 103\cdot 409\cdot 136973\cdot 1835872831815206461 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.7.437137538929872152263330629707930008528.1 x23 - 3x22 + 4x20 + 5x19 - 5x18 - 14x17 + 4x16 + 15x15 + 10x14 - 22x13 - 13x12 + 16x11 + 18x10 - 3x9 - 23x8 + x7 + 13x6 + 4x5 - 7x4 - 4x3 + 5x2 + x - 1 \( 2^{4}\cdot 17\cdot 241\cdot 1709\cdot 3877\cdot 111868093\cdot 346250347\cdot 25983511363 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.1.1019554101555073829802491841336279296875.1 x23 + 23x21 + 230x19 + 1311x17 + 4692x15 + 10948x13 + 16744x11 + 16445x9 + 9867x7 + 3289x5 + 506x3 + 23x - 1 \( -\,5^{11}\cdot 23^{23} \) $F_{23}$ (as 23T4) Trivial (GRH)
23.1.1401264465406761398087443557925374656512.1 x23 - 4x - 8 \( -\,2^{26}\cdot 25811015603927\cdot 808975051375354229 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.15.9024061084396593245740482274651471479637.1 x23 - 6x22 - 5x21 + 86x20 - 45x19 - 531x18 + 490x17 + 1869x16 - 1929x15 - 4166x14 + 4062x13 + 6124x12 - 4949x11 - 5930x10 + 3501x9 + 3657x8 - 1386x7 - 1348x6 + 286x5 + 273x4 - 28x3 - 27x2 + x + 1 \( 9024061084396593245740482274651471479637 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.9.9554598217771454170076503812873306955636.1 x23 - x22 - 4x21 - 3x20 + 10x19 + 17x18 - 2x17 - 26x16 - 21x15 + 15x14 + 19x13 - 7x12 - 18x11 + 15x10 + 35x9 - 33x7 - 24x6 + 12x5 + 16x4 + 3x3 - 5x2 - 2x + 1 \( -\,2^{2}\cdot 19\cdot 432841815513398891\cdot 290448827022730856621 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.15.12400700046148013345324171691662893757500.1 x23 - 2x22 - 20x21 + 36x20 + 175x19 - 273x18 - 876x17 + 1134x16 + 2749x15 - 2812x14 - 5571x13 + 4267x12 + 7255x11 - 3939x10 - 5887x9 + 2181x8 + 2825x7 - 734x6 - 749x5 + 154x4 + 99x3 - 19x2 - 5x + 1 \( 2^{2}\cdot 5^{4}\cdot 7499\cdot 275729\cdot 49942556731\cdot 48034096151655703 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.1.22420232145752475211320750475138484404224.1 x23 + 4x - 8 \( -\,2^{30}\cdot 3\cdot 929\cdot 623071\cdot 16280269\cdot 738591239095427 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.1.28585240626865948858207093238982844088320.1 x23 + 8x - 4 \( -\,2^{22}\cdot 5\cdot 24986142523\cdot 54552257894632015274417 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.9.30040962001154759467875853831400403771043.1 x23 - 2x22 - 4x21 + 6x20 + 10x19 - 7x18 - 14x17 + 11x16 + 12x15 - 31x14 - 36x13 + 41x12 + 89x11 + 5x10 - 105x9 - 65x8 + 56x7 + 68x6 - 7x5 - 34x4 - 4x3 + 9x2 + x - 1 \( -\,508621\cdot 158113511\cdot 1092887040821\cdot 341802543194293 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.3.32143105694342279203435391034157117445401.1 x23 - 3x - 1 \( 259028266789\cdot 124091112112198565028075828709 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.1.32143105736103215203131215102867183266535.1 x23 + 3x - 1 \( -\,5\cdot 22723592653\cdot 282905139402414328282680249319 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.1.32230684745676381300120646520469073166336.1 x23 + 3x - 2 \( -\,2^{23}\cdot 17\cdot 43\cdot 67\cdot 971821\cdot 15873405731\cdot 5085469520371 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.13.425103981715298419969372518134528837127343.1 x23 - 7x22 + 2x21 + 88x20 - 150x19 - 422x18 + 1148x17 + 862x16 - 4167x15 - 105x14 + 8563x13 - 2935x12 - 10393x11 + 5920x10 + 7285x9 - 5405x8 - 2661x7 + 2503x6 + 356x5 - 537x4 + 19x3 + 39x2 - 2x - 1 \( -\,13\cdot 1289\cdot 4057217\cdot 26391289\cdot 32505503\cdot 7288751994309941 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.1.623108105251821583281000440567147642632335.1 x23 - 3x - 3 \( -\,3^{22}\cdot 5\cdot 203008301\cdot 19561943299801571525063 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.1.655248346862420849973190809665781162457231.1 x23 - 2x - 3 \( -\,587\cdot 75967200927041\cdot 14694056584644694851886093 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.1.655251210966702902606919524078263146264719.1 x23 - x - 3 \( -\,41\cdot 263\cdot 455033\cdot 133544293000689084344982443848921 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.1.655251210967044330484283743635659792988303.1 x23 - 3 \( -\,3^{22}\cdot 23^{23} \) $F_{23}$ (as 23T4) Trivial (GRH)
23.1.655251210967385758361647963193056439711887.1 x23 + x - 3 \( -\,859\cdot 1733\cdot 440165607405506986116687141540644921 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.1.687394316682267077687567046704171943344271.1 x23 + 3x - 3 \( -\,3^{22}\cdot 7\cdot 467399\cdot 10931299891\cdot 612464196024013 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.17.696771975062209357134867192571475966589863.1 x23 - 3x22 - 18x21 + 55x20 + 141x19 - 429x18 - 638x17 + 1858x16 + 1864x15 - 4889x14 - 3693x13 + 8033x12 + 4990x11 - 8160x10 - 4433x9 + 4919x8 + 2383x7 - 1652x6 - 677x5 + 297x4 + 89x3 - 27x2 - 4x + 1 \( -\,17\cdot 40986586768365256302051011327733880387639 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.1.751680528112712572094133652841196244056207.1 x23 + 9x - 9 \( -\,3^{22}\cdot 151\cdot 158631250967721112920032141873 \) $S_{23}$ (as 23T7) Trivial (GRH)
23.11.1105964546020085080320539114269649147026432.1 x23 - 7x22 + 2x21 + 88x20 - 150x19 - 422x18 + 1148x17 + 862x16 - 4167x15 - 105x14 + 8563x13 - 2935x12 - 10393x11 + 5920x10 + 7285x9 - 5405x8 - 2661x7 + 2503x6 + 354x5 - 537x4 + 18x3 + 39x2 - 2x - 1 \( 2^{10}\cdot 22483\cdot 2527336563667297\cdot 19007452217635529293 \) $S_{23}$ (as 23T7) Trivial (GRH)

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