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
12.0.2951578112000000000.1	x^12 - 4x^11 + 28x^10 - 76x^9 + 359x^8 - 772x^7 + 2662x^6 - 4216x^5 + 11540x^4 - 13284x^3 + 37260x^2 - 26468x + 52681	\( 2^{18}\cdot 5^{9}\cdot 7^{8} \)	$C_{12}$ (as 12T1)	$[146]$
12.0.3741199797824000000.1	x^12 + 33x^10 + 388x^8 + 2140x^6 + 5894x^4 + 7762x^2 + 3881	\( 2^{12}\cdot 5^{6}\cdot 3881^{3} \)	12T235	$[120]$
12.0.4970515778063137449.3	x^12 - x^11 + 44x^10 - 31x^9 + 691x^8 - 288x^7 + 4745x^6 - 300x^5 + 13879x^4 + 9649x^3 + 10628x^2 + 20959x + 41581	\( 3^{6}\cdot 7^{10}\cdot 17^{6} \)	$C_6\times C_2$ (as 12T2)	$[130]$
12.0.5351362262028177408.1	x^12 + 39x^10 + 585x^8 + 4212x^6 + 14742x^4 + 22113x^2 + 9477	\( 2^{12}\cdot 3^{6}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	$[2, 2, 26]$
12.0.6485674202367523969.1	x^12 - 4x^11 + 25x^10 - 68x^9 + 325x^8 - 686x^7 + 2604x^6 - 4075x^5 + 13689x^4 - 14393x^3 + 44782x^2 - 23610x + 73319	\( 13^{10}\cdot 19^{6} \)	$C_6\times C_2$ (as 12T2)	$[117]$
12.0.7942684196931961856.1	x^12 - x^11 + 3x^10 - 3x^9 + 8x^8 - 10x^7 + 22x^6 - 20x^5 + 32x^4 - 24x^3 + 48x^2 - 32x + 64	\( 2^{10}\cdot 1409\cdot 2346271^{2} \)	12T293	$[101]$
12.0.8822943478336000000.4	x^12 - 2x^11 + 21x^10 - 32x^9 + 279x^8 - 358x^7 + 2390x^6 - 2390x^5 + 13837x^4 - 9964x^3 + 50382x^2 - 20104x + 90481	\( 2^{12}\cdot 5^{6}\cdot 13^{10} \)	$C_6\times C_2$ (as 12T2)	$[4, 4, 8]$
12.0.9120030452383481856.1	x^12 + x^10 + x^8 + 9x^6 + 4x^4 + 16x^2 + 64	\( 2^{20}\cdot 3^{2}\cdot 37^{2}\cdot 163^{4} \)	$C_2^2\times C_2^2:S_4$ (as 12T139)	$[126]$
12.0.9687897476476640001.1	x^12 - 4x^11 + 23x^10 - 64x^9 + 312x^8 - 632x^7 + 2493x^6 - 3780x^5 + 13720x^4 - 11802x^3 + 50834x^2 - 14525x + 89971	\( 3^{6}\cdot 7^{10}\cdot 19^{6} \)	$C_6\times C_2$ (as 12T2)	$[168]$
12.0.10331448031704891637.2	x^12 - x^11 + x^10 - 27x^9 + 27x^8 - 183x^7 + 326x^6 + 649x^5 + 131x^4 - 573x^3 + 1782x^2 - 2133x + 4941	\( 7^{8}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	$[111]$
12.0.13179165217344000000.2	x^12 + 55x^10 + 1177x^8 + 12263x^6 + 63001x^4 + 137703x^2 + 63001	\( 2^{12}\cdot 3^{6}\cdot 5^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	$[2, 52]$
12.0.13179165217344000000.3	x^12 - 2x^11 + 19x^10 - 26x^9 + 260x^8 - 364x^7 + 2388x^6 - 2590x^5 + 14491x^4 - 13666x^3 + 62305x^2 - 40136x + 118441	\( 2^{12}\cdot 3^{6}\cdot 5^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	$[2, 156]$
12.0.13179165217344000000.5	x^12 - 6x^11 + 51x^10 - 200x^9 + 978x^8 - 2778x^7 + 9197x^6 - 18642x^5 + 45309x^4 - 62422x^3 + 108054x^2 - 79542x + 163549	\( 2^{12}\cdot 3^{6}\cdot 5^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	$[4, 52]$ (GRH)
12.0.13179165217344000000.6	x^12 + 35x^10 + 875x^8 + 10500x^6 + 91875x^4 + 306250x^2 + 765625	\( 2^{12}\cdot 3^{6}\cdot 5^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	$[2, 52]$
12.0.13179165217344000000.7	x^12 + 15x^10 + 225x^8 + 3375x^6 + 50625x^4 + 759375x^2 + 11390625	\( 2^{12}\cdot 3^{6}\cdot 5^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	$[2, 52]$
12.0.13179165217344000000.9	x^12 - 2x^11 - x^10 - 2x^9 + 100x^8 - 204x^7 + 20x^6 - 390x^5 + 4243x^4 - 5206x^3 + 5381x^2 + 10088x + 28561	\( 2^{12}\cdot 3^{6}\cdot 5^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	$[2, 52]$
12.0.13179165217344000000.10	x^12 - 6x^11 + 25x^10 - 70x^9 + 257x^8 - 674x^7 + 1805x^6 - 3284x^5 + 8459x^4 - 12124x^3 + 24313x^2 - 18702x + 48721	\( 2^{12}\cdot 3^{6}\cdot 5^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	$[2, 52]$
12.0.13334335014735765625.1	x^12 - 4x^11 + 27x^10 - 68x^9 + 396x^8 - 934x^7 + 4774x^6 - 9889x^5 + 37692x^4 - 54863x^3 + 153377x^2 - 115667x + 250879	\( 5^{6}\cdot 7^{8}\cdot 23^{6} \)	$C_6\times C_2$ (as 12T2)	$[3, 117]$ (GRH)
12.0.14118999709877436672.1	x^12 - x^11 + 3x^10 - x^9 + 4x^8 + 10x^6 + 16x^4 - 8x^3 + 48x^2 - 32x + 64	\( 2^{8}\cdot 3^{2}\cdot 113\cdot 7364131^{2} \)	12T293	$[102]$
12.0.14881778037403916432.1	x^12 - x^11 + 4x^10 - 3x^9 + 12x^8 - 6x^7 + 23x^6 - 12x^5 + 48x^4 - 24x^3 + 64x^2 - 32x + 64	\( 2^{4}\cdot 12113\cdot 8762773^{2} \)	12T293	$[105]$
12.0.15110084652576306192.1	x^12 - 2x^11 + 4x^10 - 5x^9 + 6x^8 - 5x^7 + 11x^6 - 10x^5 + 24x^4 - 40x^3 + 64x^2 - 64x + 64	\( 2^{4}\cdot 3^{2}\cdot 1549^{2}\cdot 2657\cdot 4057^{2} \)	12T293	$[128]$
12.0.15484949423558175888.1	x^12 - 2x^11 + 6x^10 - 9x^9 + 20x^8 - 25x^7 + 45x^6 - 50x^5 + 80x^4 - 72x^3 + 96x^2 - 64x + 64	\( 2^{4}\cdot 3^{2}\cdot 1657\cdot 8055869^{2} \)	12T293	$[104]$
12.0.16998231738349085968.1	x^12 - x^11 + 4x^10 - 3x^9 + 10x^8 - 6x^7 + 23x^6 - 12x^5 + 40x^4 - 24x^3 + 64x^2 - 32x + 64	\( 2^{4}\cdot 19^{2}\cdot 10273\cdot 535229^{2} \)	12T293	$[107]$
12.0.17213603549184000000.2	x^12 - 2x^11 + 23x^10 - 42x^9 + 377x^8 - 430x^7 + 4372x^6 - 2306x^5 + 32791x^4 - 7712x^3 + 141770x^2 - 16004x + 276121	\( 2^{18}\cdot 3^{6}\cdot 5^{6}\cdot 7^{8} \)	$C_6\times C_2$ (as 12T2)	$[228]$ (GRH)
12.0.20408004397065968761.1	x^12 - 4x^11 + 31x^10 - 88x^9 + 480x^8 - 1046x^7 + 4500x^6 - 7261x^5 + 27052x^4 - 29227x^3 + 99169x^2 - 53803x + 177113	\( 13^{10}\cdot 23^{6} \)	$C_6\times C_2$ (as 12T2)	$[252]$
12.0.21303969908600640625.2	x^12 - 4x^11 + 43x^10 - 112x^9 + 748x^8 - 1200x^7 + 6649x^6 - 4588x^5 + 36700x^4 - 9786x^3 + 141674x^2 - 70165x + 271181	\( 5^{6}\cdot 7^{10}\cdot 13^{6} \)	$C_6\times C_2$ (as 12T2)	$[4, 4, 20]$ (GRH)
12.0.22039921152000000000.1	x^12 + 18x^10 - 4x^9 + 234x^8 + 36x^7 + 1738x^6 + 72x^5 + 8355x^4 + 3624x^3 + 40764x^2 + 21732x + 70471	\( 2^{18}\cdot 3^{16}\cdot 5^{9} \)	$C_{12}$ (as 12T1)	$[218]$ (GRH)
12.0.22435920541265661952.1	x^12 + 3x^10 + 8x^8 - 2x^7 + 18x^6 - 4x^5 + 32x^4 + 48x^2 + 64	\( 2^{12}\cdot 2017\cdot 1647931^{2} \)	12T293	$[144]$
12.0.22579948934773140625.1	x^12 - 4x^11 - x^10 + 10x^9 + 103x^8 - 172x^7 + 707x^6 - 250x^5 + 4471x^4 - 2724x^3 + 17649x^2 - 7080x + 35495	\( 5^{6}\cdot 11^{6}\cdot 13^{8} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 42]$
12.0.25735133446455103488.1	x^12 - 2x^11 + 3x^10 - 2x^9 + 2x^8 + 4x^7 - 6x^6 + 8x^5 + 8x^4 - 16x^3 + 48x^2 - 64x + 64	\( 2^{12}\cdot 3^{2}\cdot 313\cdot 1493447^{2} \)	12T293	$[110]$ (GRH)
12.0.26345168059215642624.1	x^12 - 2x^11 + 27x^10 - 42x^9 + 419x^8 - 538x^7 + 4136x^6 - 4132x^5 + 26950x^4 - 19172x^3 + 108501x^2 - 42258x + 211303	\( 2^{18}\cdot 3^{6}\cdot 13^{10} \)	$C_6\times C_2$ (as 12T2)	$[2, 182]$ (GRH)
12.0.26345168059215642624.7	x^12 + 14x^10 + 8x^8 - 888x^6 - 384x^4 + 10624x^2 + 40000	\( 2^{18}\cdot 3^{6}\cdot 13^{10} \)	$C_6\times C_2$ (as 12T2)	$[104]$
12.0.26859533924753868137.1	x^12 + 3x^10 - x^9 + 7x^8 - 5x^7 + 17x^6 - 10x^5 + 28x^4 - 8x^3 + 48x^2 + 64	\( 79^{2}\cdot 6833\cdot 793627^{2} \)	12T293	$[141]$ (GRH)
12.0.27927616772217573376.3	x^12 + 15x^10 + 169x^8 + 1527x^6 + 8625x^4 + 26083x^2 + 32761	\( 2^{12}\cdot 7^{10}\cdot 17^{6} \)	$C_6\times C_2$ (as 12T2)	$[3, 60]$ (GRH)
12.0.29218823485775015625.1	x^12 - 6x^11 + 45x^10 - 150x^9 + 636x^8 - 1230x^7 + 3551x^6 - 2436x^5 + 14157x^4 - 6522x^3 + 61566x^2 - 50892x + 94429	\( 3^{18}\cdot 5^{6}\cdot 13^{6} \)	$C_6\times C_2$ (as 12T2)	$[152]$ (GRH)
12.0.30484209987928082169.1	x^12 - 4x^11 + 29x^10 - 84x^9 + 461x^8 - 976x^7 + 4353x^6 - 6772x^5 + 27208x^4 - 25046x^3 + 110223x^2 - 37447x + 213487	\( 3^{6}\cdot 7^{10}\cdot 23^{6} \)	$C_6\times C_2$ (as 12T2)	$[234]$ (GRH)
12.0.30705314996019351568.1	x^12 - x^11 + 3x^10 - 2x^9 + 9x^8 - 5x^7 + 17x^6 - 10x^5 + 36x^4 - 16x^3 + 48x^2 - 32x + 64	\( 2^{4}\cdot 59^{2}\cdot 7297\cdot 274867^{2} \)	12T293	$[173]$ (GRH)
12.0.31643295525096890625.1	x^12 + 9x^10 - 4x^9 + 183x^8 + 36x^7 + 2281x^6 + 1200x^5 + 17949x^4 + 5580x^3 + 77817x^2 + 5118x + 156329	\( 3^{16}\cdot 5^{6}\cdot 19^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 2, 2, 12]$
12.0.33103510137573028416.1	x^12 - x^11 + 4x^10 - 5x^9 + 10x^8 - 16x^7 + 23x^6 - 32x^5 + 40x^4 - 40x^3 + 64x^2 - 32x + 64	\( 2^{6}\cdot 3^{2}\cdot 569\cdot 10050083^{2} \)	12T293	$[120]$ (GRH)
12.0.33620319432000000000.1	x^12 - 4x^11 + 43x^10 - 126x^9 + 814x^8 - 1852x^7 + 8517x^6 - 14386x^5 + 51505x^4 - 61084x^3 + 200870x^2 - 138098x + 354061	\( 2^{12}\cdot 3^{6}\cdot 5^{9}\cdot 7^{8} \)	$C_{12}$ (as 12T1)	$[2, 194]$ (GRH)
12.0.33695156183620386816.59	x^12 + 12x^10 - 12x^8 + 64x^6 - 48x^4 + 192x^2 + 64	\( 2^{30}\cdot 3^{22} \)	$C_2\times C_2^2:S_4$ (as 12T103)	$[2, 2, 28]$
12.0.34644013976823922064.1	x^12 + 4x^10 - x^9 + 10x^8 - 5x^7 + 21x^6 - 10x^5 + 40x^4 - 8x^3 + 64x^2 + 64	\( 2^{4}\cdot 11489\cdot 13728181^{2} \)	12T293	$[130]$ (GRH)
12.0.34896906600120140625.1	x^12 - 3x^11 + 9x^10 + 46x^9 - 48x^8 + 312x^7 + 371x^6 + 171x^5 - 3597x^4 + 14402x^3 + 31740x^2 - 122784x + 161344	\( 3^{18}\cdot 5^{6}\cdot 7^{8} \)	$C_6\times C_2$ (as 12T2)	$[111]$
12.0.36099543110378323968.1	x^12 - 4x^11 + 34x^10 - 96x^9 + 487x^8 - 1060x^7 + 3402x^6 - 5164x^5 + 10378x^4 - 10924x^3 + 38696x^2 - 30344x + 53857	\( 2^{33}\cdot 3^{6}\cdot 7^{8} \)	$C_{12}$ (as 12T1)	$[194]$ (GRH)
12.0.37435196904948681689.1	x^12 - x^11 + 3x^10 - 2x^9 + 6x^8 - 8x^7 + 19x^6 - 16x^5 + 24x^4 - 16x^3 + 48x^2 - 32x + 64	\( 47\cdot 103^{3}\cdot 853759^{2} \)	12T293	$[102]$ (GRH)
12.0.38303288464389083136.1	x^12 + 9x^10 + 132x^8 + 2011x^6 + 14085x^4 + 44814x^2 + 54289	\( 2^{12}\cdot 3^{18}\cdot 17^{6} \)	$C_6\times C_2$ (as 12T2)	$[4, 4, 12]$ (GRH)
12.0.39032490004709953424.1	x^12 - x^11 - x^10 + 7x^8 - 3x^7 - 5x^6 - 6x^5 + 28x^4 - 16x^2 - 32x + 64	\( 2^{4}\cdot 163^{2}\cdot 569\cdot 401707^{2} \)	12T293	$[130]$ (GRH)
12.0.39450497360817629200.1	x^12 - x^11 + 4x^10 - 5x^9 + 10x^8 - 12x^7 + 23x^6 - 24x^5 + 40x^4 - 40x^3 + 64x^2 - 32x + 64	\( 2^{4}\cdot 5^{2}\cdot 31\cdot 223\cdot 3777139^{2} \)	12T293	$[134]$ (GRH)
12.0.42276719146699894672.1	x^12 - x^11 + 3x^10 - 2x^9 + 7x^8 - 5x^7 + 19x^6 - 10x^5 + 28x^4 - 16x^3 + 48x^2 - 32x + 64	\( 2^{4}\cdot 6217\cdot 20615801^{2} \)	12T293	$[117]$ (GRH)
12.0.42528831343005192192.1	x^12 + 38x^10 + 562x^8 + 4042x^6 + 14204x^4 + 20475x^2 + 5397	\( 2^{12}\cdot 3^{3}\cdot 7^{3}\cdot 257^{5} \)	$C_4^2.D_{12}$ (as 12T151)	$[2, 2, 42]$

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