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 106)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.37681663399442934481.1	x^12 - 2x^11 + 17x^10 - 28x^9 + 138x^8 - 157x^7 + 549x^6 - 382x^5 + 1099x^4 - 77x^3 + 1016x^2 + 9x + 1912	\( 1831^{6} \)	$\PSL(2,11)$ (as 12T179)	$[20]$
12.0.188210093521191571456.1	x^12 - 6x^11 + 33x^10 - 110x^9 + 297x^8 - 594x^7 + 1023x^6 - 1210x^5 + 2090x^4 - 1144x^3 + 1100x^2 + 408x + 280	\( 2^{12}\cdot 11^{16} \)	$\PSL(2,11)$ (as 12T179)	$[4]$ (GRH)
12.0.4053179721535836749649.1	x^12 - x^11 + 11x^10 - 44x^9 + 176x^8 - 495x^7 + 1122x^6 - 2838x^5 + 8195x^4 - 18524x^3 + 29876x^2 - 29773x + 14329	\( 3^{6}\cdot 11^{18} \)	$\PSL(2,11)$ (as 12T179)	$[4]$ (GRH)
12.0.38384832176270862188544.1	x^12 - 22x^10 + 385x^8 - 1144x^7 + 1364x^6 - 1144x^5 + 1892x^4 - 2112x^3 + 880x^2 - 1264x + 1540	\( 2^{24}\cdot 3^{6}\cdot 11^{12} \)	$\PSL(2,11)$ (as 12T179)	$[2, 2, 2]$ (GRH)
12.0.51792700544612326478169.1	x^12 - 3x^11 - 12x^10 + 103x^9 - 159x^8 - 498x^7 + 2406x^6 - 4188x^5 + 3405x^4 + 358x^3 - 585x^2 - 4821x + 4939	\( 3^{14}\cdot 101^{8} \)	$\PSL(2,11)$ (as 12T179)	$[20]$ (GRH)
12.0.192727135765700169170944.1	x^12 - 2x^11 + 33x^10 - 110x^9 + 550x^8 - 1606x^7 + 4719x^6 - 6798x^5 + 16764x^4 - 1782x^3 + 15411x^2 - 4002x + 1063	\( 2^{22}\cdot 11^{16} \)	$\PSL(2,11)$ (as 12T179)	$[2]$ (GRH)
12.0.311268212838585865361664.1	x^12 - 6x^11 + 33x^10 - 66x^9 + 330x^8 - 462x^7 + 4213x^6 + 9834x^5 + 35706x^4 + 30822x^3 + 78969x^2 + 24042x + 51625	\( 2^{8}\cdot 3^{18}\cdot 11^{12} \)	$\PSL(2,11)$ (as 12T179)	$[12]$ (GRH)
12.0.364374741057026882338816.1	x^12 - 4x^11 + 44x^10 - 88x^9 + 627x^8 - 660x^7 + 4928x^6 - 2024x^5 + 26851x^4 + 1848x^3 + 84568x^2 + 7960x + 116209	\( 2^{16}\cdot 11^{18} \)	$\PSL(2,11)$ (as 12T179)	$[2]$ (GRH)
12.0.1457498964228107529355264.1	x^12 - 4x^11 + 44x^9 - 154x^8 - 308x^7 + 3300x^6 - 9064x^5 + 13640x^4 - 10560x^3 + 4290x^2 - 1852x + 863	\( 2^{18}\cdot 11^{18} \)	$\PSL(2,11)$ (as 12T179)	$[2]$ (GRH)
12.0.23319983427649720469684224.1	x^12 - 4x^11 + 44x^10 + 253x^8 + 3872x^7 - 4840x^6 + 31944x^5 - 9317x^4 - 305404x^3 + 760364x^2 - 1124904x + 1138599	\( 2^{22}\cdot 11^{18} \)	$\PSL(2,11)$ (as 12T179)	$[2]$ (GRH)
12.0.93279933710598881878736896.1	x^12 - 4x^11 - 22x^10 + 132x^9 + 55x^8 - 1980x^7 + 5698x^6 - 4268x^5 - 8866x^4 + 14344x^3 + 26136x^2 - 50912x + 28616	\( 2^{24}\cdot 11^{18} \)	$\PSL(2,11)$ (as 12T179)	$[2, 2]$ (GRH)
12.0.140498081973195423325618176.1	x^12 - 4x^11 - 22x^10 + 495x^8 + 880x^7 - 2596x^6 - 16016x^5 - 16885x^4 + 47212x^3 + 212586x^2 + 310968x + 234385	\( 2^{22}\cdot 3^{6}\cdot 11^{16} \)	$\PSL(2,11)$ (as 12T179)	$[2, 2]$ (GRH)
12.0.140498081973195423325618176.2	x^12 - 132x^9 - 143x^8 - 264x^7 + 7744x^6 + 34848x^5 + 162019x^4 + 473352x^3 + 1066736x^2 + 1633764x + 1494955	\( 2^{22}\cdot 3^{6}\cdot 11^{16} \)	$\PSL(2,11)$ (as 12T179)	$[2, 2]$ (GRH)
12.0.140498081973195423325618176.3	x^12 - 4x^11 + 66x^10 - 308x^9 + 1331x^8 - 2904x^7 + 6248x^6 + 37840x^5 + 141999x^4 + 173756x^3 + 537526x^2 + 334932x + 259089	\( 2^{22}\cdot 3^{6}\cdot 11^{16} \)	$\PSL(2,11)$ (as 12T179)	$[2, 2]$ (GRH)
12.0.265629186230572597224996864.1	x^12 - 4x^11 + 11x^10 + 88x^9 - 176x^8 + 1320x^7 + 3003x^6 - 4158x^5 + 141768x^4 - 19602x^3 - 350757x^2 - 803034x + 2459241	\( 2^{16}\cdot 3^{6}\cdot 11^{18} \)	$\PSL(2,11)$ (as 12T179)	$[2, 2]$ (GRH)
12.0.566646488794154535342833664.1	x^12 - 6x^11 + 33x^10 - 66x^9 + 660x^8 - 1782x^7 + 8261x^6 - 41250x^5 + 90288x^4 - 143286x^3 + 300069x^2 - 151362x + 109935	\( 2^{22}\cdot 3^{16}\cdot 11^{12} \)	$\PSL(2,11)$ (as 12T179)	$[6]$ (GRH)
12.0.711271539989301830585942016.1	x^12 - 4x^11 + 396x^8 - 1056x^7 + 2112x^6 + 52272x^4 - 69696x^3 + 278784x^2 - 211968x + 2336832	\( 2^{18}\cdot 3^{10}\cdot 11^{16} \)	$\PSL(2,11)$ (as 12T179)	Trivial (GRH)
12.0.1217022540466101928754937856.1	x^12 - 2x^11 - 27x^10 + 290x^9 + 188x^8 - 4694x^7 + 547x^6 - 8986x^5 + 131774x^4 + 14830x^3 - 349217x^2 - 636126x + 1791401	\( 2^{22}\cdot 31^{6}\cdot 83^{6} \)	$\PSL(2,11)$ (as 12T179)	$[2, 2, 10]$ (GRH)
12.0.1344747755292273773451546624.1	x^12 - 6x^11 + 66x^10 - 220x^9 + 1947x^8 - 3564x^7 + 21714x^6 + 15774x^5 + 179157x^4 + 30272x^3 + 337128x^2 + 682584x + 449476	\( 2^{12}\cdot 3^{10}\cdot 11^{18} \)	$\PSL(2,11)$ (as 12T179)	$[2]$ (GRH)
12.0.8101827385190641164017995776.1	x^12 - 6x^11 - 66x^10 + 286x^9 + 3399x^8 - 5676x^7 - 99836x^6 - 61182x^5 + 1822986x^4 + 889020x^3 - 4970790x^2 - 39556944x + 77021757	\( 2^{12}\cdot 3^{16}\cdot 11^{16} \)	$\PSL(2,11)$ (as 12T179)	$[12]$ (GRH)
12.0.8101827385190641164017995776.2	x^12 - 132x^9 + 726x^8 - 1716x^7 + 28952x^6 - 4092x^5 + 1261161x^4 + 2610564x^3 + 1638648x^2 - 46951920x + 63954000	\( 2^{12}\cdot 3^{16}\cdot 11^{16} \)	$\PSL(2,11)$ (as 12T179)	$[12]$ (GRH)
12.0.17000267918756646222399799296.1	x^12 - 4x^11 - 110x^10 - 220x^9 + 4455x^8 + 23848x^7 + 38104x^6 - 15488x^5 - 27005x^4 + 150876x^3 - 37818x^2 - 334404x + 249705	\( 2^{22}\cdot 3^{6}\cdot 11^{18} \)	$\PSL(2,11)$ (as 12T179)	$[2, 2]$ (GRH)
12.0.45521378559315317157500289024.1	x^12 - 4x^11 - 22x^10 + 220x^9 + 66x^8 - 528x^7 + 7920x^6 - 61248x^5 + 443652x^4 - 615472x^3 + 5326024x^2 - 1735376x + 25818824	\( 2^{24}\cdot 3^{10}\cdot 11^{16} \)	$\PSL(2,11)$ (as 12T179)	$[2, 2]$ (GRH)
12.0.86063856338705521500898983936.1	x^12 + 726x^8 + 39930x^6 - 31944x^5 + 578985x^4 - 351384x^3 + 263538x^2 - 159720x + 131769	\( 2^{18}\cdot 3^{10}\cdot 11^{18} \)	$\PSL(2,11)$ (as 12T179)	$[2, 2]$ (GRH)
12.0.86063856338705521500898983936.2	x^12 - 4x^11 + 66x^10 - 396x^9 + 594x^8 - 594x^7 + 3564x^6 + 10692x^5 - 29403x^4 + 16038x^3 - 304722x^2 + 100602x + 2989629	\( 2^{18}\cdot 3^{10}\cdot 11^{18} \)	$\PSL(2,11)$ (as 12T179)	$[2, 2]$ (GRH)
12.0.86063856338705521500898983936.3	x^12 - 4x^11 + 132x^10 - 264x^9 + 3498x^8 + 2376x^7 - 1716x^6 + 166320x^5 + 325809x^4 + 78012x^3 + 11855448x^2 + 16309080x + 5679756	\( 2^{18}\cdot 3^{10}\cdot 11^{18} \)	$\PSL(2,11)$ (as 12T179)	$[4]$ (GRH)
12.0.86063856338705521500898983936.4	x^12 - 4x^11 + 88x^10 - 528x^9 + 1848x^8 - 14652x^7 + 145860x^6 - 897336x^5 + 5076852x^4 - 19653392x^3 + 49941848x^2 - 102293600x + 136284024	\( 2^{18}\cdot 3^{10}\cdot 11^{18} \)	$\PSL(2,11)$ (as 12T179)	Trivial (GRH)
12.0.117631308450744732160000000000.1	x^12 - 2x^11 - 33x^10 + 330x^9 - 18986x^7 + 74327x^6 + 276078x^5 - 2839925x^4 + 9074560x^3 + 40925434x^2 - 156371568x + 143707588	\( 2^{18}\cdot 5^{10}\cdot 11^{16} \)	$\PSL(2,11)$ (as 12T179)	$[2]$ (GRH)
12.0.117631308450744732160000000000.2	x^12 - 4x^11 + 88x^10 + 550x^9 + 1265x^8 + 37708x^7 + 150788x^6 + 731434x^5 + 4744410x^4 + 9416770x^3 + 56589346x^2 + 74954206x + 75216153	\( 2^{18}\cdot 5^{10}\cdot 11^{16} \)	$\PSL(2,11)$ (as 12T179)	Trivial (GRH)
12.0.117631308450744732160000000000.3	x^12 + 44x^10 - 110x^9 + 2585x^8 - 9372x^7 + 70840x^6 - 196218x^5 + 857890x^4 - 1586970x^3 + 4347266x^2 - 6275810x + 2894749	\( 2^{18}\cdot 5^{10}\cdot 11^{16} \)	$\PSL(2,11)$ (as 12T179)	Trivial (GRH)
12.12.175754771514233266263796181449.1	x^12 - 4x^11 - 202x^10 + 750x^9 + 14320x^8 - 57987x^7 - 420190x^6 + 2051347x^5 + 3470883x^4 - 27131426x^3 + 31354680x^2 - 1044099x - 6047919	\( 74843^{6} \)	$\PSL(2,11)$ (as 12T179)	$[5]$ (GRH)
12.0.222396692539689259240000000000.1	x^12 - 2x^11 + 11x^10 + 440x^9 + 55x^8 - 9922x^7 + 9394x^6 + 325138x^5 + 2461635x^4 + 8129220x^3 + 13245771x^2 + 10626358x + 3509901	\( 2^{12}\cdot 5^{10}\cdot 11^{18} \)	$\PSL(2,11)$ (as 12T179)	$[2]$ (GRH)
12.0.551430626404538014225974837504.1	x^12 - 3x^11 - 407x^9 + 1716x^8 + 1221x^7 + 5203x^6 - 281622x^5 + 2387946x^4 + 2142756x^3 - 58182696x^2 - 41320152x + 646853244	\( 2^{8}\cdot 3^{18}\cdot 11^{18} \)	$\PSL(2,11)$ (as 12T179)	$[12]$ (GRH)
12.0.551430626404538014225974837504.2	x^12 - 6x^11 + 33x^10 + 440x^9 - 99x^8 + 4554x^7 + 97911x^6 + 415008x^5 + 1179882x^4 + 5680664x^3 + 22980408x^2 + 46856388x + 37309780	\( 2^{8}\cdot 3^{18}\cdot 11^{18} \)	$\PSL(2,11)$ (as 12T179)	$[12]$ (GRH)
12.0.551430626404538014225974837504.3	x^12 - 3x^11 - 66x^10 - 143x^9 + 4950x^8 - 6435x^7 - 28215x^6 - 483912x^5 + 1995840x^4 + 6173992x^3 - 21351792x^2 - 66441360x + 214378768	\( 2^{8}\cdot 3^{18}\cdot 11^{18} \)	$\PSL(2,11)$ (as 12T179)	$[12]$ (GRH)
12.0.980321113608067580846177488896.1	x^12 + 66x^10 - 264x^9 + 2178x^8 - 12342x^7 + 67760x^6 - 293304x^5 + 1140183x^4 - 3637986x^3 + 8409258x^2 - 12431826x + 8504001	\( 2^{12}\cdot 3^{16}\cdot 11^{18} \)	$\PSL(2,11)$ (as 12T179)	$[12]$ (GRH)
12.0.8296271242435216551954427674624.1	x^12 - 6x^11 + 165x^10 - 770x^9 + 12936x^8 - 47190x^7 + 427669x^6 - 1032306x^5 + 7052364x^4 - 12733446x^3 + 69797673x^2 - 78320898x + 266210415	\( 2^{22}\cdot 3^{16}\cdot 11^{16} \)	$\PSL(2,11)$ (as 12T179)	$[6]$ (GRH)
12.0.14233388322540112591360000000000.1	x^12 + 1210x^8 + 66550x^6 - 159720x^5 + 1217865x^4 - 1756920x^3 + 732050x^2 + 3354120x + 3294225	\( 2^{18}\cdot 5^{10}\cdot 11^{18} \)	$\PSL(2,11)$ (as 12T179)	Trivial (GRH)
12.0.15685137817729081293538839822336.1	x^12 - 132x^10 - 792x^9 + 9768x^8 + 27984x^7 - 106656x^6 - 535920x^5 + 4900368x^4 - 9843328x^3 + 9291216x^2 + 777312x + 19395024	\( 2^{16}\cdot 3^{16}\cdot 11^{18} \)	$\PSL(2,11)$ (as 12T179)	$[6]$ (GRH)
12.0.33185084969740866207817710698496.1	x^12 - 66x^10 - 396x^9 + 2046x^8 + 22176x^7 + 44000x^6 - 491040x^5 - 2099592x^4 + 2860704x^3 + 52313184x^2 + 106043904x + 74124864	\( 2^{24}\cdot 3^{16}\cdot 11^{16} \)	$\PSL(2,11)$ (as 12T179)	$[2, 6]$ (GRH)
12.0.74666441181916948967589849071616.1	x^12 - 132x^10 + 9108x^8 - 353100x^6 - 228096x^5 + 7781400x^4 + 8667648x^3 - 103926240x^2 - 111912192x + 1259471268	\( 2^{22}\cdot 3^{18}\cdot 11^{16} \)	$\PSL(2,11)$ (as 12T179)	$[2, 6]$ (GRH)
12.0.74666441181916948967589849071616.2	x^12 - 6x^11 + 33x^10 - 110x^9 + 2112x^8 - 7854x^7 + 24013x^6 - 35442x^5 + 1081080x^4 - 2029698x^3 + 1589841x^2 + 6368382x + 214386723	\( 2^{22}\cdot 3^{18}\cdot 11^{16} \)	$\PSL(2,11)$ (as 12T179)	$[2, 6]$ (GRH)
12.0.564664961438246926567398233604096.1	x^12 + 66x^10 - 2332x^9 - 1683x^8 - 9504x^7 + 1098504x^6 - 967824x^5 + 16259463x^4 + 97123400x^3 + 85826268x^2 + 428379792x + 2961900172	\( 2^{18}\cdot 3^{18}\cdot 11^{18} \)	$\PSL(2,11)$ (as 12T179)	$[2, 6]$ (GRH)
12.0.1003848820334661202786485748629504.1	x^12 - 4356x^8 + 47916x^6 - 2156220x^4 + 256158936x^2 - 186297408x + 42693156	\( 2^{22}\cdot 3^{16}\cdot 11^{18} \)	$\PSL(2,11)$ (as 12T179)	$[6]$ (GRH)
12.0.4015395281338644811145942994518016.1	x^12 + 2178x^8 - 383328x^6 - 539055x^4 + 1024635744x^2 - 17139361536x + 90338718096	\( 2^{24}\cdot 3^{16}\cdot 11^{18} \)	$\PSL(2,11)$ (as 12T179)	$[2, 6]$ (GRH)
12.0.4015395281338644811145942994518016.2	x^12 + 264x^10 - 660x^9 + 23958x^8 - 123420x^7 + 625328x^6 - 4461996x^5 + 15987609x^4 - 49073244x^3 + 227670696x^2 - 358726104x + 806177988	\( 2^{24}\cdot 3^{16}\cdot 11^{18} \)	$\PSL(2,11)$ (as 12T179)	$[2, 6]$ (GRH)
12.0.36138557532047803300313486950662144.1	x^12 - 264x^10 - 2200x^9 + 13068x^8 + 252648x^7 + 1788864x^6 + 9774864x^5 + 42937092x^4 + 127832144x^3 + 301295808x^2 + 517880352x + 573460624	\( 2^{24}\cdot 3^{18}\cdot 11^{18} \)	$\PSL(2,11)$ (as 12T179)	$[2, 2, 6]$ (GRH)
12.0.769311739390426167457490080964882209.1	x^12 - 2x^11 - 15x^10 + 648x^9 - 3778x^8 - 10924x^7 + 198008x^6 - 1005130x^5 - 799775x^4 + 34602694x^3 - 81144849x^2 - 327865899x + 1084940875	\( 19^{6}\cdot 23^{6}\cdot 101^{10} \)	$\PSL(2,11)$ (as 12T179)	$[2, 2, 20]$ (GRH)
12.12.393262136091127324453858365845510721649.1	x^12 - 2x^11 - 443x^10 + 1088x^9 + 72628x^8 - 200348x^7 - 5362636x^6 + 15311536x^5 + 171815284x^4 - 456652720x^3 - 1812709328x^2 + 3130627879x + 2339838952	\( 13^{6}\cdot 59^{6}\cdot 3529^{6} \)	$\PSL(2,11)$ (as 12T179)	$[2, 10]$ (GRH)
12.0.44968021684696030092752233382638572407809.1	x^12 - 2x^11 + 193x^10 - 72x^9 + 14438x^8 + 19996x^7 + 538148x^6 + 1611514x^5 + 11374585x^4 + 39039918x^3 + 142645595x^2 + 299173773x + 208327555	\( 5963263^{6} \)	$\PSL(2,11)$ (as 12T179)	$[20]$ (GRH)