Global number field search results

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Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying matches 1-50 of 121)

Label	Polynomial	Discriminant	Galois group	Class group
23.1.8316624386164136054632388935703.1	x^23 - 2x^22 - 3x^21 + 13x^20 - 19x^19 + 21x^18 - 75x^16 + 202x^15 - 378x^14 + 596x^13 - 798x^12 + 955x^11 - 995x^10 + 849x^9 - 610x^8 + 384x^7 - 151x^6 + 2x^5 + 46x^4 - 37x^3 + 3x^2 + 20x + 1	\( -\,647^{11} \)	$D_{23}$ (as 23T2)	Trivial (GRH)
23.1.20539040122483692476958386186983.1	x^23 - x - 1	\( -\,29\cdot 53264767\cdot 13296646221023838475181 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.1523249425950439235855871175083439.1	x^23 + 4x^21 - 14x^20 + 25x^19 - 6x^18 - 14x^17 - 26x^16 + 31x^15 + 48x^14 - 62x^13 + 19x^12 + 19x^11 + 24x^10 - 17x^9 + 34x^8 + 40x^7 - 228x^6 + 76x^5 + 4x^4 + 28x^3 + 45x^2 + 49x + 1	\( -\,1039^{11} \)	$D_{23}$ (as 23T2)	Trivial (GRH)
23.1.2939886993377131174870795633320047.1	x^23 + 5x^21 - 17x^20 + 33x^19 - 14x^18 + 53x^17 - 34x^16 - 19x^15 + 140x^14 - 19x^13 + 257x^12 - 106x^11 - 16x^10 + 274x^9 + 165x^8 + 515x^7 - 28x^6 + 129x^5 + 89x^4 + 524x^3 + 244x^2 + 50x - 1	\( -\,1103^{11} \)	$D_{23}$ (as 23T2)	Trivial (GRH)
23.1.14982213765271379362645677088782079.1	x^23 - 7x^22 + 15x^21 - 6x^20 + x^19 - 21x^18 + 17x^17 + 2x^16 + 46x^15 - 10x^14 + 108x^13 - 129x^12 - 98x^11 - 144x^10 - 85x^9 + 8x^8 + 187x^7 - 82x^6 + 363x^5 + 216x^4 - 128x^3 - 51x^2 + 77x - 1	\( -\,1279^{11} \)	$D_{23}$ (as 23T2)	Trivial (GRH)
23.1.58230945563524325903440619509366903.1	x^23 - 2x^22 + 16x^21 - 34x^20 + 68x^19 - 63x^18 + 17x^17 + 43x^16 - 139x^15 + 165x^14 + 25x^13 - 228x^12 + 265x^11 - 270x^10 + 75x^9 + 246x^8 - 130x^7 - 161x^6 + 240x^5 - 393x^4 + 569x^3 - 385x^2 + 99x + 1	\( -\,1447^{11} \)	$D_{23}$ (as 23T2)	Trivial (GRH)
23.1.69781355284066743169711357773860671.1	x^23 - 5x^22 + 3x^21 + 3x^20 + 43x^19 - 6x^18 - 31x^17 - 56x^16 - 68x^15 - 89x^14 + 147x^13 + 180x^12 + 274x^11 + 240x^10 - 211x^9 - 521x^8 - 383x^7 - 275x^6 + 291x^5 + 249x^4 + 358x^3 - 9x^2 + 107x + 1	\( -\,1471^{11} \)	$D_{23}$ (as 23T2)	Trivial (GRH)
23.1.100388389417020021246100166894420339.1	x^23 - 3x^21 - 6x^20 + x^19 + 17x^18 + 18x^17 - 10x^16 - 43x^15 - 25x^14 + 33x^13 + 60x^12 + 11x^11 - 54x^10 - 47x^9 + 12x^8 + 46x^7 + 17x^6 - 17x^5 - 16x^4 + 6x^2 + x - 1	\( -\,167\cdot 30727\cdot 499717\cdot 39149185505838967853863 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.459177995857290463522143518056811108.1	x^23 - 2x^22 - x^21 + 5x^20 - x^19 - 4x^18 + 6x^15 + 6x^14 - 17x^13 - 10x^12 + 31x^11 + 5x^10 - 32x^9 + 25x^7 - 17x^5 + 2x^4 + 9x^3 - 3x^2 - 2x + 1	\( -\,2^{2}\cdot 1021\cdot 425123\cdot 264472629367076822658099919 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.687231335140465279781021461534970411.1	x^23 - 3x^22 + 7x^21 - 8x^20 - 11x^19 + 19x^18 + 160x^17 + 291x^16 + 464x^15 - 35x^14 - 648x^13 - 1313x^12 - 1101x^11 - 240x^10 + 1477x^9 + 1043x^8 + 863x^7 - 10x^6 - 264x^5 - 712x^4 - 80x^3 - 2304x^2 - 2048x - 1024	\( -\,1811^{11} \)	$D_{23}$ (as 23T2)	Trivial (GRH)
23.1.1670424922585164788805622697952280576.1	x^23 - 4x - 4	\( -\,2^{22}\cdot 8623\cdot 10045730659\cdot 4597557191821267 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.1823491470737247969166873376199879779.1	x^23 - 11x^22 + 47x^21 - 78x^20 - 51x^19 + 367x^18 - 359x^17 - 364x^16 + 1182x^15 - 712x^14 - 1586x^13 + 3310x^12 - 393x^11 - 5271x^10 + 5059x^9 + 3246x^8 - 8091x^7 - 125x^6 + 10047x^5 - 6818x^4 - 2608x^3 + 2872x^2 + 1488x - 2176	\( -\,1979^{11} \)	$D_{23}$ (as 23T2)	Trivial (GRH)
23.1.2864125503948510940846004233663441639.1	x^23 + 2x - 1	\( -\,127\cdot 5892521806212607\cdot 3827252586261454951 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.10367471077843902113690154634909319168.1	x^23 + 4x - 4	\( -\,2^{22}\cdot 127\cdot 121259\cdot 78283735681\cdot 2050329605299 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.76122611959712052465607572442400686080.1	x^23 - 8x - 8	\( -\,2^{22}\cdot 3\cdot 5\cdot 557\cdot 2100359171059\cdot 1034221960670111 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.84714925830153585744409482078292279296.1	x^23 - 2x - 2	\( -\,2^{22}\cdot 3\cdot 5519\cdot 1219883568588480577372817507 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.87579030112206219473123894560276086784.1	x^23 - x - 2	\( -\,2^{23}\cdot 7\cdot 24177221\cdot 78687506363\cdot 783971054543 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.87579030453634015434594065117161697047.1	x^23 - x - 4	\( -\,7901\cdot 159683\cdot 69415968602603755097356934209 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.87579030453634096837343451956922810368.1	x^23 - 2	\( -\,2^{22}\cdot 23^{23} \)	$F_{23}$ (as 23T4)	Trivial (GRH)
23.1.90443135077114607930277421835553341440.1	x^23 + 2x - 2	\( -\,2^{22}\cdot 5\cdot 9629\cdot 78977\cdot 5671055267529396512759 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.99035448947556141209079331471444934656.1	x^23 + 8x - 8	\( -\,2^{22}\cdot 19\cdot 2617\cdot 310741\cdot 1528181322635255601073 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.332434202154298684636783958613993659679.1	x^23 - 9x - 9	\( -\,3^{22}\cdot 103\cdot 409\cdot 136973\cdot 1835872831815206461 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.1019554101555073829802491841336279296875.1	x^23 + 23x^21 + 230x^19 + 1311x^17 + 4692x^15 + 10948x^13 + 16744x^11 + 16445x^9 + 9867x^7 + 3289x^5 + 506x^3 + 23x - 1	\( -\,5^{11}\cdot 23^{23} \)	$F_{23}$ (as 23T4)	Trivial (GRH)
23.1.1401264465406761398087443557925374656512.1	x^23 - 4x - 8	\( -\,2^{26}\cdot 25811015603927\cdot 808975051375354229 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.22420232145752475211320750475138484404224.1	x^23 + 4x - 8	\( -\,2^{30}\cdot 3\cdot 929\cdot 623071\cdot 16280269\cdot 738591239095427 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.28585240626865948858207093238982844088320.1	x^23 + 8x - 4	\( -\,2^{22}\cdot 5\cdot 24986142523\cdot 54552257894632015274417 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.32143105736103215203131215102867183266535.1	x^23 + 3x - 1	\( -\,5\cdot 22723592653\cdot 282905139402414328282680249319 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.32230684745676381300120646520469073166336.1	x^23 + 3x - 2	\( -\,2^{23}\cdot 17\cdot 43\cdot 67\cdot 971821\cdot 15873405731\cdot 5085469520371 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.623108105251821583281000440567147642632335.1	x^23 - 3x - 3	\( -\,3^{22}\cdot 5\cdot 203008301\cdot 19561943299801571525063 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.655248346862420849973190809665781162457231.1	x^23 - 2x - 3	\( -\,587\cdot 75967200927041\cdot 14694056584644694851886093 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.655251210966702902606919524078263146264719.1	x^23 - x - 3	\( -\,41\cdot 263\cdot 455033\cdot 133544293000689084344982443848921 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.655251210967044330484283743635659792988303.1	x^23 - 3	\( -\,3^{22}\cdot 23^{23} \)	$F_{23}$ (as 23T4)	Trivial (GRH)
23.1.655251210967385758361647963193056439711887.1	x^23 + x - 3	\( -\,859\cdot 1733\cdot 440165607405506986116687141540644921 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.687394316682267077687567046704171943344271.1	x^23 + 3x - 3	\( -\,3^{22}\cdot 7\cdot 467399\cdot 10931299891\cdot 612464196024013 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.751680528112712572094133652841196244056207.1	x^23 + 9x - 9	\( -\,3^{22}\cdot 151\cdot 158631250967721112920032141873 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.2227978859786797789863805466564380466715471.1	x^23 + 7x - 4	\( -\,3\cdot 661\cdot 102898348801\cdot 10918926580157025647925153137 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.3673330748836946834207458969827592925872128.1	x^23 - 2x - 4	\( -\,2^{42}\cdot 3\cdot 3739\cdot 360193\cdot 400051\cdot 516740936139647 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.24025938536396056832371480539091058917638144.1	x^23 + 4x - 2	\( -\,2^{22}\cdot 3\cdot 13\cdot 449\cdot 327121816425619441138711330723201 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.24681102168332647528758926939274761787816079.1	x^23 + 4x - 3	\( -\,114089\cdot 350671093\cdot 18936502114367\cdot 32577747177637381 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.91833270152975982595442020712674762462068736.1	x^23 + 2x - 4	\( -\,2^{42}\cdot 40227185812367\cdot 519063606886319927 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.367300934642084084154053706613660659067387904.1	x^23 - 3x - 4	\( -\,2^{22}\cdot 10301\cdot 19433\cdot 437464575526593257842019918297 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.367332107351407118355062992998527724684540747.1	x^23 - 5x - 8	\( -\,3\cdot 41\cdot 567183743783102484853\cdot 5265383449191308483213 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.367333077747799306901175587167342331456630551.1	x^23 - x - 8	\( -\,13\cdot 251\cdot 3046418117488903\cdot 36953319274301480913105359 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.367333077747799648329134354136286567864467456.1	x^23 + x - 4	\( -\,2^{22}\cdot 3\cdot 859\cdot 887\cdot 31627\cdot 276929\cdot 4374572903952274742317 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.367333077755462820493791710147614510732598339.1	x^23 + 3x - 8	\( -\,23036001684392168053\cdot 15946043188751196471887063 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.865004941741938633917747707002884268046728983.1	x^23 - 23x^20 + 184x^19 - 1334x^18 + 3680x^17 - 7567x^16 + 3381x^15 + 48346x^14 - 105455x^13 + 165048x^12 - 1033942x^11 + 3237457x^10 - 6694426x^9 + 24074675x^8 - 57748676x^7 + 58090042x^6 - 24771506x^5 + 67771087x^4 - 75769360x^3 + 19385596x^2 - 386078x + 1437601	\( -\,23^{33} \)	$D_{23}$ (as 23T2)	Trivial (GRH)
23.1.1017534389230254627325036709335862989230702592.1	x^23 + 5x - 2	\( -\,2^{22}\cdot 31\cdot 97\cdot 31026973\cdot 2773405960861\cdot 937568290656913 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.4070137469342008936134049847912034355032910567.1	x^23 + 5x - 1	\( -\,7\cdot 17\cdot 53\cdot 1307\cdot 188072810621797\cdot 2625334491870023904395339 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.4070792720552955099996534283743635659792988303.1	x^23 + 5x - 3	\( -\,509\cdot 7997628134681640667969615488690836266783867 \)	$S_{23}$ (as 23T7)	Trivial (GRH)
23.1.4437470547089787362567306989916729171217743872.1	x^23 + 5x - 4	\( -\,2^{22}\cdot 29\cdot 43\cdot 1669\cdot 8233\cdot 15257051\cdot 4046914931701778759797 \)	$S_{23}$ (as 23T7)	Trivial (GRH)