Global number field search results

Further refine search

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

Results (displaying all 14 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.2.99714188227072000000000.1	x^18 - 4x^17 - 3x^16 + 28x^15 - 11x^14 - 62x^13 + 40x^12 + 42x^11 - 22x^10 + 26x^9 - 9x^8 - 16x^7 - 73x^6 - 154x^5 - 29x^4 - 2x^3 - 44x^2 - 8x - 1	\( 2^{18}\cdot 5^{9}\cdot 41^{7} \)	18T273	$[2]$
18.2.694051978812799525584896.1	x^18 + 4x^16 + 31x^14 + 66x^12 + 171x^10 + 328x^8 - 615x^6 - 742x^4 + 1020x^2 - 776	\( 2^{33}\cdot 97^{7} \)	18T273	$[2]$
18.0.3882077770175991570051072.1	x^18 + 6x^16 + 15x^14 + 18x^12 - 3x^10 - 27x^8 + 42x^6 + 174x^4 + 162x^2 + 43	\( -\,2^{12}\cdot 3^{20}\cdot 43^{7} \)	18T273	Trivial
18.0.6241137136607730639252951.1	x^18 + 6x^16 - 3x^15 + 3x^14 + 42x^13 - 99x^12 + 189x^11 - 90x^10 - 245x^9 + 774x^8 - 1059x^7 + 1029x^6 - 714x^5 + 381x^4 - 153x^3 + 45x^2 - 9x + 1	\( -\,3^{20}\cdot 151^{7} \)	18T273	Trivial
18.4.39748423601695422066720768.1	x^18 + 12x^16 + 42x^14 + 36x^12 - 27x^10 - 360x^8 - 108x^6 + 720x^4 - 540x^2 + 288	\( -\,2^{47}\cdot 3^{24} \)	18T273	Trivial
18.4.124470130898370390617227264.1	x^18 - 4x^16 - 16x^15 + 12x^14 + 28x^13 + 46x^12 - 148x^11 - 100x^10 + 332x^9 - 358x^8 + 1196x^7 - 1730x^6 - 136x^5 + 2332x^4 - 2208x^3 + 664x^2 + 128x - 80	\( -\,2^{35}\cdot 167^{7} \)	18T273	$[2]$
18.0.568234047317888519287109375.1	x^18 - 5x^17 + 15x^16 - 24x^15 + 45x^14 - 75x^13 + 90x^12 - 90x^11 + 115x^10 - 135x^9 + 115x^8 - 90x^7 + 90x^6 - 75x^5 + 45x^4 - 24x^3 + 15x^2 - 5x + 1	\( -\,5^{15}\cdot 211^{7} \)	18T273	$[4]$
18.0.2543899110508507012270129152.1	x^18 - 6x^16 + 12x^14 + 36x^12 - 60x^10 + 84x^8 + 384x^6 + 156x^4 - 33x^2 + 2	\( -\,2^{53}\cdot 3^{24} \)	18T273	Trivial (GRH)
18.10.25240988693802106655672448843776.1	x^18 - 24x^16 - 58x^15 + 106x^14 + 934x^13 + 1273x^12 - 2726x^11 - 6419x^10 + 5718x^9 + 31255x^8 + 16092x^7 - 76469x^6 - 103520x^5 + 16460x^4 + 76942x^3 + 13067x^2 - 14598x - 3113	\( 2^{27}\cdot 2113^{7} \)	18T273	$[2]$ (GRH)
18.10.25240988693802106655672448843776.2	x^18 - 8x^17 + 2x^16 + 78x^15 - 236x^14 + 174x^13 + 387x^12 - 1298x^11 + 1474x^10 - 590x^9 - 1213x^8 + 2362x^7 - 1396x^6 + 594x^5 + 889x^4 - 822x^3 + 93x^2 + 22x - 1	\( 2^{27}\cdot 2113^{7} \)	18T273	$[2]$ (GRH)
18.6.977451593654185513757539842392064.1	x^18 - 27x^16 - 12x^15 + 444x^14 + 402x^13 - 4452x^12 - 6324x^11 + 18438x^10 + 48230x^9 + 3204x^8 - 149436x^7 - 208398x^6 + 35346x^5 + 232134x^4 + 462792x^3 + 709707x^2 - 17022x - 453719	\( 2^{26}\cdot 3^{20}\cdot 11^{15} \)	18T273	$[2]$ (GRH)
18.6.1615423276403334825963036726001664.1	x^18 - 6x^17 - 3x^16 + 126x^15 - 522x^14 + 772x^13 + 1553x^12 - 6344x^11 + 6485x^10 + 11506x^9 - 153869x^8 + 214254x^7 + 906829x^6 - 1164534x^5 - 2575296x^4 + 2823590x^3 + 2247322x^2 - 1644880x - 792713	\( 2^{33}\cdot 2113^{7} \)	18T273	$[2]$ (GRH)
18.18.3983824820086231599411024626450432.1	x^18 - 83x^16 - 38x^15 + 2667x^14 + 2088x^13 - 42105x^12 - 40668x^11 + 345676x^10 + 343620x^9 - 1456925x^8 - 1222186x^7 + 3006365x^6 + 1557206x^5 - 2558391x^4 - 357902x^3 + 723633x^2 - 108198x - 7523	\( 2^{18}\cdot 19^{7}\cdot 137^{9} \)	18T273	Trivial (GRH)
18.18.5763065516728982926781941659467776.1	x^18 - 4x^17 - 66x^16 + 216x^15 + 1834x^14 - 4388x^13 - 27644x^12 + 41344x^11 + 240608x^10 - 171108x^9 - 1197004x^8 + 121428x^7 + 3186428x^6 + 1072936x^5 - 3857520x^4 - 2467112x^3 + 1240320x^2 + 1082912x + 99896	\( 2^{18}\cdot 17^{9}\cdot 293^{7} \)	18T273	$[4]$ (GRH)