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 )

Label	Polynomial	Discriminant	Galois group	Class group
12.0.25955658105272205078125.1	x^12 - x^11 + 163x^10 - 164x^9 + 9854x^8 - 10018x^7 + 283912x^6 - 311604x^5 + 4213235x^4 - 4872746x^3 + 32079035x^2 - 27964467x + 110528251	\( 5^{9}\cdot 7^{10}\cdot 19^{6} \)	$C_{12}$ (as 12T1)	$[2, 4, 1636]$ (GRH)
12.0.28888480797518767578125.1	x^12 - x^11 + 128x^10 - 36x^9 + 6953x^8 + 1688x^7 + 205004x^6 + 100734x^5 + 3493011x^4 + 1447263x^3 + 32886288x^2 + 7087687x + 134106701	\( 5^{9}\cdot 7^{8}\cdot 37^{6} \)	$C_{12}$ (as 12T1)	$[37, 370]$ (GRH)
12.0.31373472824750103330816.5	x^12 + 156x^10 + 9126x^8 + 246064x^6 + 2998905x^4 + 13366548x^2 + 4826809	\( 2^{24}\cdot 3^{18}\cdot 13^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 5418]$ (GRH)
12.0.33511670005535928548329.4	x^12 - 4x^11 + 115x^10 - 368x^9 + 5800x^8 - 14486x^7 + 163344x^6 - 302185x^5 + 2706834x^4 - 3326843x^3 + 25059307x^2 - 15437955x + 101631179	\( 13^{10}\cdot 79^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 2, 6, 210]$ (GRH)
12.0.35172055560068186443776.1	x^12 + 63x^10 + 2049x^8 + 44131x^6 + 604521x^4 + 4582623x^2 + 14417209	\( 2^{12}\cdot 3^{18}\cdot 53^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 4, 1260]$ (GRH)
12.0.43925697850453056000000.5	x^12 - 6x^11 + 141x^10 - 650x^9 + 7494x^8 - 26142x^7 + 185303x^6 - 467076x^5 + 2246907x^4 - 3744586x^3 + 12300264x^2 - 10501650x + 32319541	\( 2^{12}\cdot 3^{18}\cdot 5^{6}\cdot 11^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 2548]$ (GRH)
12.0.50010143639414923828125.1	x^12 - 3x^11 + 99x^10 - 291x^9 + 4425x^8 - 12288x^7 + 111738x^6 - 258864x^5 + 1615344x^4 - 2617004x^3 + 12629298x^2 - 11707065x + 44340281	\( 3^{16}\cdot 5^{9}\cdot 29^{6} \)	$C_{12}$ (as 12T1)	$[2, 5378]$ (GRH)
12.0.53483214216056720703125.1	x^12 - x^11 + 143x^10 - 41x^9 + 8623x^8 + 2028x^7 + 280434x^6 + 136924x^5 + 5232016x^4 + 2217128x^3 + 53594968x^2 + 12100257x + 236593391	\( 5^{9}\cdot 7^{8}\cdot 41^{6} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 2, 2, 436]$ (GRH)
12.0.53981860730241024000000.12	x^12 + 100x^10 + 3973x^8 + 79976x^6 + 865846x^4 + 5025864x^2 + 15816529	\( 2^{24}\cdot 3^{6}\cdot 5^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 10, 260]$ (GRH)
12.0.59779054097312062075641.4	x^12 - 4x^11 + 127x^10 - 408x^9 + 7040x^8 - 17686x^7 + 217076x^6 - 404221x^5 + 3923740x^4 - 4854123x^3 + 39465521x^2 - 24466635x + 173113225	\( 3^{6}\cdot 13^{10}\cdot 29^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 6, 1314]$ (GRH)
12.0.61464734415837024654213.1	x^12 - x^11 + 183x^10 - 183x^9 + 12923x^8 - 12923x^7 + 440987x^6 - 440987x^5 + 7432699x^4 - 7432699x^3 + 56374683x^2 - 56374683x + 154258651	\( 3^{6}\cdot 13^{11}\cdot 19^{6} \)	$C_{12}$ (as 12T1)	$[2, 38, 190]$ (GRH)
12.0.64022047012554352623616.6	x^12 - 2x^11 + 123x^10 - 202x^9 + 6739x^8 - 8858x^7 + 208872x^6 - 208260x^5 + 3847558x^4 - 2612324x^3 + 39868309x^2 - 13964626x + 181540151	\( 2^{18}\cdot 11^{6}\cdot 13^{10} \)	$C_6\times C_2$ (as 12T2)	$[3, 9, 468]$ (GRH)
12.0.81672801965256564453125.1	x^12 - x^11 + 198x^10 - 199x^9 + 14544x^8 - 14743x^7 + 508507x^6 - 554959x^5 + 9098780x^4 - 10507816x^3 + 82172540x^2 - 73475842x + 324352981	\( 5^{9}\cdot 7^{10}\cdot 23^{6} \)	$C_{12}$ (as 12T1)	$[5, 50, 50]$ (GRH)
12.0.81701572994888000000000.1	x^12 - 4x^11 + 163x^10 - 526x^9 + 10934x^8 - 27772x^7 + 382237x^6 - 724306x^5 + 7349105x^4 - 9390924x^3 + 76289310x^2 - 50833538x + 338937061	\( 2^{12}\cdot 5^{9}\cdot 7^{8}\cdot 11^{6} \)	$C_{12}$ (as 12T1)	$[2, 2, 4034]$ (GRH)
12.0.83615035344190272000000.1	x^12 + 195x^10 + 14625x^8 + 526500x^6 + 9213750x^4 + 69103125x^2 + 148078125	\( 2^{12}\cdot 3^{6}\cdot 5^{6}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 2, 2, 436]$ (GRH)
12.0.87726396011200183795712.1	x^12 - 4x^11 + 130x^10 - 416x^9 + 6567x^8 - 16420x^7 + 155274x^6 - 285164x^5 + 1713002x^4 - 2100652x^3 + 10909864x^2 - 7513800x + 31017889	\( 2^{33}\cdot 7^{8}\cdot 11^{6} \)	$C_{12}$ (as 12T1)	$[3, 4710]$ (GRH)
12.0.92332774415743512085357.1	x^12 - x^11 + 196x^10 - 196x^9 + 14821x^8 - 14821x^7 + 541321x^6 - 541321x^5 + 9755071x^4 - 9755071x^3 + 78858196x^2 - 78858196x + 226936321	\( 13^{11}\cdot 61^{6} \)	$C_{12}$ (as 12T1)	$[52, 260]$ (GRH)
12.0.95632159177126518718464.15	x^12 + 242x^10 + 21296x^8 + 830544x^6 + 14055360x^4 + 82458112x^2 + 113379904	\( 2^{18}\cdot 3^{6}\cdot 7^{10}\cdot 11^{6} \)	$C_6\times C_2$ (as 12T2)	$[52, 312]$ (GRH)
12.0.95632159177126518718464.16	x^12 - 2x^11 + 121x^10 - 196x^9 + 6618x^8 - 8728x^7 + 207374x^6 - 214002x^5 + 3900776x^4 - 2880444x^3 + 41712696x^2 - 17138192x + 196996801	\( 2^{18}\cdot 3^{6}\cdot 7^{10}\cdot 11^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 6076]$ (GRH)
12.0.105433321738752000000000.1	x^12 + 210x^10 + 16380x^8 + 604800x^6 + 11113200x^4 + 95256000x^2 + 285768000	\( 2^{18}\cdot 3^{6}\cdot 5^{9}\cdot 7^{10} \)	$C_{12}$ (as 12T1)	$[2, 2, 3970]$ (GRH)
12.0.112015891613143986328125.1	x^12 + 168x^10 - x^9 + 9774x^8 - 1701x^7 + 257648x^6 - 137187x^5 + 3288795x^4 - 3206849x^3 + 21932874x^2 - 17829192x + 76909321	\( 3^{18}\cdot 5^{9}\cdot 23^{6} \)	$C_{12}$ (as 12T1)	$[2, 8770]$ (GRH)
12.0.114391518299003180548096.2	x^12 + 204x^10 + 15317x^8 + 510952x^6 + 7182806x^4 + 34076568x^2 + 24137569	\( 2^{24}\cdot 7^{10}\cdot 17^{6} \)	$C_6\times C_2$ (as 12T2)	$[4, 3612]$ (GRH)
12.0.119680300997734464000000.5	x^12 + 81x^10 + 3228x^8 + 81283x^6 + 1286037x^4 + 11367462x^2 + 42211009	\( 2^{12}\cdot 3^{18}\cdot 5^{6}\cdot 13^{6} \)	$C_6\times C_2$ (as 12T2)	$[6, 3192]$ (GRH)
12.0.121637404636973946372096.2	x^12 - 6x^11 + 63x^10 - 260x^9 + 1995x^8 - 6486x^7 + 39033x^6 - 95424x^5 + 490488x^4 - 829016x^3 + 3879852x^2 - 3480240x + 14609528	\( 2^{18}\cdot 3^{16}\cdot 47^{6} \)	$C_6\times C_2$ (as 12T2)	$[3, 3660]$ (GRH)
12.0.124863324110553424564224.6	x^12 + 253x^10 + 23276x^8 + 949026x^6 + 16790460x^4 + 102981488x^2 + 148035889	\( 2^{12}\cdot 3^{6}\cdot 7^{10}\cdot 23^{6} \)	$C_6\times C_2$ (as 12T2)	$[4, 4368]$ (GRH)
12.0.124907309945634636693504.6	x^12 - 4x^11 + 94x^10 - 296x^9 + 3960x^8 - 9788x^7 + 95942x^6 - 178764x^5 + 1398035x^4 - 1774428x^3 + 11439684x^2 - 7514692x + 40657609	\( 2^{24}\cdot 3^{6}\cdot 7^{8}\cdot 11^{6} \)	$C_6\times C_2$ (as 12T2)	$[3, 6, 936]$ (GRH)
12.0.143546083959041477185536.1	x^12 - 6x^11 + 105x^10 - 470x^9 + 4686x^8 - 15990x^7 + 115139x^6 - 291360x^5 + 1651035x^4 - 2834218x^3 + 13126680x^2 - 11755602x + 45581077	\( 2^{12}\cdot 3^{18}\cdot 67^{6} \)	$C_6\times C_2$ (as 12T2)	$[10062]$ (GRH)
12.0.156890269550137684525056.5	x^12 + 204x^10 + 15606x^8 + 550256x^6 + 8769705x^4 + 51114852x^2 + 24137569	\( 2^{24}\cdot 3^{18}\cdot 17^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 4, 4, 364]$ (GRH)
12.0.160588926796425169739008.1	x^12 - 2x^11 + 236x^10 - 235x^9 + 17355x^8 + 3606x^7 + 526541x^6 + 764610x^5 + 7985835x^4 + 12614627x^3 + 52558187x^2 + 49019641x + 91733851	\( 2^{8}\cdot 13^{6}\cdot 37^{9} \)	$C_3 : C_4$ (as 12T5)	$[2, 2, 2, 16, 80]$ (GRH)
12.0.186694177220038656000000.14	x^12 - 6x^11 + 177x^10 - 830x^9 + 11814x^8 - 42342x^7 + 367625x^6 - 958098x^5 + 5597562x^4 - 9646066x^3 + 38478141x^2 - 33807978x + 119894041	\( 2^{18}\cdot 3^{18}\cdot 5^{6}\cdot 7^{6} \)	$C_6\times C_2$ (as 12T2)	$[4, 3484]$ (GRH)
12.0.193406657670994185947997.1	x^12 - x^11 + 222x^10 - 222x^9 + 19007x^8 - 19007x^7 + 785435x^6 - 785435x^5 + 15986257x^4 - 15986257x^3 + 145193244x^2 - 145193244x + 458981641	\( 3^{6}\cdot 13^{11}\cdot 23^{6} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 2692]$ (GRH)
12.0.193873788090710808693921.2	x^12 - 6x^11 - 9x^10 + 72x^9 + 204x^8 - 600x^7 + 832x^6 + 1203x^5 + 10530x^4 - 10089x^3 + 41817x^2 - 14205x + 157375	\( 3^{18}\cdot 7^{10}\cdot 11^{6} \)	$C_6\times C_2$ (as 12T2)	$[6, 24, 72]$ (GRH)
12.0.203279051316071044583424.1	x^12 - 6x^11 + 111x^10 - 500x^9 + 5235x^8 - 18006x^7 + 135691x^6 - 346086x^5 + 2048187x^4 - 3539604x^3 + 17104653x^2 - 15389676x + 62195361	\( 2^{12}\cdot 3^{18}\cdot 71^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 2, 2, 10, 210]$ (GRH)
12.0.208332854832557470253056.1	x^12 - 2x^11 - 49x^10 + 50x^9 + 975x^8 - 318x^7 - 5152x^6 + 9584x^5 + 18694x^4 - 34388x^3 + 140349x^2 - 100962x + 250587	\( 2^{18}\cdot 7^{8}\cdot 13^{10} \)	$C_6\times C_2$ (as 12T2)	$[3, 4221]$ (GRH)
12.0.215715056426865017578125.1	x^12 - 3x^11 + 129x^10 - 381x^9 + 7305x^8 - 20358x^7 + 228508x^6 - 535884x^5 + 4054374x^4 - 6735844x^3 + 38602548x^2 - 36067335x + 160801651	\( 3^{16}\cdot 5^{9}\cdot 37^{6} \)	$C_{12}$ (as 12T1)	$[2, 14, 910]$ (GRH)
12.0.222957405416602891976704.4	x^12 + 228x^10 + 19133x^8 + 713336x^6 + 11207606x^4 + 59426376x^2 + 47045881	\( 2^{24}\cdot 7^{10}\cdot 19^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 8190]$ (GRH)
12.0.222957405416602891976704.6	x^12 + 128x^10 + 6493x^8 + 166076x^6 + 2261086x^4 + 16095776x^2 + 58232161	\( 2^{24}\cdot 7^{10}\cdot 19^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 4030]$ (GRH)
12.0.239020026860167472611328.1	x^12 - 4x^11 + 154x^10 - 496x^9 + 9167x^8 - 23140x^7 + 254842x^6 - 473884x^5 + 3306578x^4 - 4102284x^3 + 23868696x^2 - 16329464x + 75924577	\( 2^{33}\cdot 7^{8}\cdot 13^{6} \)	$C_{12}$ (as 12T1)	$[2, 34, 170]$ (GRH)
12.0.240148397880610960674816.1	x^12 + 93x^10 + 4164x^8 + 115271x^6 + 1988841x^4 + 19219578x^2 + 78446449	\( 2^{12}\cdot 3^{18}\cdot 73^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 2, 2, 2, 364]$ (GRH)
12.0.246168290724753398765625.2	x^12 - x^11 + 62x^10 - 226x^9 + 577x^8 - 2377x^7 - 3136x^6 + 12956x^5 + 79168x^4 + 61904x^3 + 194304x^2 + 378688x + 235264	\( 3^{6}\cdot 5^{6}\cdot 43^{10} \)	$C_6\times C_2$ (as 12T2)	$[16226]$ (GRH)
12.0.249556896876602205078125.1	x^12 - x^11 + 188x^10 - 56x^9 + 14713x^8 + 3228x^7 + 612804x^6 + 294994x^5 + 14417911x^4 + 6384683x^3 + 183583288x^2 + 45546027x + 995262101	\( 5^{9}\cdot 7^{8}\cdot 53^{6} \)	$C_{12}$ (as 12T1)	$[19330]$ (GRH)
12.0.260560131209473946812416.8	x^12 - 6x^11 + 81x^10 - 350x^9 + 2868x^8 - 9438x^7 + 52261x^6 - 125154x^5 + 550392x^4 - 902538x^3 + 2888181x^2 - 2456298x + 13749723	\( 2^{18}\cdot 3^{6}\cdot 7^{10}\cdot 13^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 6, 6, 84]$ (GRH)
12.0.260560131209473946812416.12	x^12 + 286x^10 + 29744x^8 + 1370928x^6 + 27418560x^4 + 190102016x^2 + 308915776	\( 2^{18}\cdot 3^{6}\cdot 7^{10}\cdot 13^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 4, 4, 684]$ (GRH)
12.0.260560131209473946812416.13	x^12 - 2x^11 + 145x^10 - 236x^9 + 9374x^8 - 12376x^7 + 343470x^6 - 352786x^5 + 7487488x^4 - 5450860x^3 + 91961560x^2 - 36698912x + 495287521	\( 2^{18}\cdot 3^{6}\cdot 7^{10}\cdot 13^{6} \)	$C_6\times C_2$ (as 12T2)	$[6, 12, 12, 36]$ (GRH)
12.0.260575062921050587398144.3	x^12 + 96x^10 - 56x^9 + 3786x^8 - 4536x^7 + 74498x^6 - 130200x^5 + 924369x^4 - 1441552x^3 + 6626874x^2 - 2382072x + 20331721	\( 2^{18}\cdot 3^{18}\cdot 37^{6} \)	$C_6\times C_2$ (as 12T2)	$[4, 4, 1008]$ (GRH)
12.0.271215206617378764238693.1	x^12 - x^11 + 235x^10 - 235x^9 + 21295x^8 - 21295x^7 + 931087x^6 - 931087x^5 + 20036719x^4 - 20036719x^3 + 191987407x^2 - 191987407x + 634146319	\( 13^{11}\cdot 73^{6} \)	$C_{12}$ (as 12T1)	$[2, 2, 5986]$ (GRH)
12.0.286051027323963456000000.5	x^12 - 6x^11 + 123x^10 - 560x^9 + 4758x^8 - 15738x^7 + 53621x^6 - 108066x^5 + 285141x^4 - 407446x^3 + 715986x^2 - 527814x + 1184689	\( 2^{12}\cdot 3^{6}\cdot 5^{6}\cdot 19^{10} \)	$C_6\times C_2$ (as 12T2)	$[2, 14, 392]$ (GRH)
12.0.293503986178850203226001.2	x^12 - 6x^11 - 9x^10 + 72x^9 + 267x^8 - 1902x^7 + 5473x^6 - 23556x^5 + 63324x^4 - 74832x^3 + 243648x^2 - 117504x + 18432	\( 3^{16}\cdot 7^{10}\cdot 17^{6} \)	$C_6\times C_2$ (as 12T2)	$[3, 3, 1365]$ (GRH)
12.0.305790568690397158047744.6	x^12 + 228x^10 + 19494x^8 + 768208x^6 + 13683705x^4 + 89139564x^2 + 47045881	\( 2^{24}\cdot 3^{18}\cdot 19^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 4, 8, 504]$ (GRH)
12.0.312360518047666176000000.6	x^12 - 6x^11 + 75x^10 - 320x^9 + 2751x^8 - 9150x^7 + 61213x^6 - 152892x^5 + 862788x^4 - 1480824x^3 + 7474092x^2 - 6757728x + 30496904	\( 2^{18}\cdot 3^{16}\cdot 5^{6}\cdot 11^{6} \)	$C_6\times C_2$ (as 12T2)	$[7, 7, 504]$ (GRH)

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