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 30 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.4.8187922952619753996288.1	x^18 + 3x^16 - 21x^12 - 27x^10 - 27x^8 - 45x^6 + 27	\( -\,2^{30}\cdot 3^{27} \)	18T366	Trivial
18.4.10834375376002294480896.2	x^18 - 4x^16 + 5x^14 + x^12 - 7x^10 + 6x^8 - 8x^6 + 9x^4 - 5x^2 + 1	\( -\,2^{30}\cdot 3^{6}\cdot 7^{12} \)	18T366	Trivial
18.2.37720649252098625605632.1	x^18 - 4x^17 + 8x^16 - 22x^15 + 35x^14 - 50x^13 + 93x^12 - 38x^11 + 89x^10 + 96x^9 - 114x^8 + 292x^7 - 272x^6 + 300x^5 - 129x^4 + 182x^3 - 27x^2 + 90x - 27	\( 2^{12}\cdot 3^{6}\cdot 7^{12}\cdot 97^{3} \)	18T366	Trivial
18.2.37720649252098625605632.2	x^18 - x^17 - 3x^16 + 2x^15 + 8x^14 - 13x^13 + 10x^12 + 19x^11 - 77x^10 + 17x^9 + 156x^8 - 128x^7 - 78x^6 + 137x^5 - 50x^4 + 67x^3 + 10x^2 - 100x - 41	\( 2^{12}\cdot 3^{6}\cdot 7^{12}\cdot 97^{3} \)	18T366	Trivial
18.0.1592822467387587324542976.1	x^18 - 4x^17 + 14x^16 - 18x^15 + 13x^14 + 86x^13 - 211x^12 + 570x^11 - 879x^10 + 1818x^9 - 1924x^8 + 116x^7 + 9116x^6 - 24970x^5 + 42769x^4 - 48268x^3 + 37263x^2 - 17494x + 4271	\( -\,2^{24}\cdot 3^{6}\cdot 7^{12}\cdot 97^{2} \)	18T366	Trivial
18.0.1592822467387587324542976.2	x^18 - 8x^16 + 5x^14 + 123x^12 - 429x^10 + 110x^8 + 2474x^6 - 4089x^4 - 3395x^2 + 9409	\( -\,2^{24}\cdot 3^{6}\cdot 7^{12}\cdot 97^{2} \)	18T366	$[2]$
18.12.5852021141154776996728512.1	x^18 - 3x^17 - 6x^16 + 24x^15 - 15x^14 + 27x^13 - 12x^12 - 261x^11 + 222x^10 + 508x^9 - 384x^8 - 534x^7 + 258x^6 + 330x^5 - 63x^4 - 102x^3 + 12x + 1	\( -\,2^{6}\cdot 3^{31}\cdot 23^{6} \)	18T366	Trivial (GRH)
18.12.6734506738465099277161408.1	x^18 - 7x^17 + 11x^16 + 30x^15 - 110x^14 + 58x^13 + 159x^12 - 212x^11 + 115x^10 - 264x^9 + 351x^8 + 98x^7 - 587x^6 + 506x^5 - 98x^4 - 109x^3 + 74x^2 - 16x + 1	\( -\,2^{6}\cdot 7^{15}\cdot 53^{6} \)	18T366	Trivial (GRH)
18.6.43006206619464857762660352.1	x^18 - 18x^16 - 2x^15 + 120x^14 + 76x^13 - 328x^12 - 936x^11 - 348x^10 + 5596x^9 + 4708x^8 - 17480x^7 - 16084x^6 + 24128x^5 + 37392x^4 + 4216x^3 - 29336x^2 - 25040x - 8168	\( 2^{24}\cdot 3^{9}\cdot 7^{12}\cdot 97^{2} \)	18T366	Trivial (GRH)
18.6.43006206619464857762660352.2	x^18 - 6x^16 - 12x^15 + x^14 - 4x^13 - 81x^12 + 164x^11 + 1709x^10 + 1608x^9 - 6866x^8 - 15686x^7 + 5518x^6 + 36380x^5 + 12519x^4 - 11030x^3 - 6651x^2 - 1802x - 83	\( 2^{24}\cdot 3^{9}\cdot 7^{12}\cdot 97^{2} \)	18T366	Trivial (GRH)
18.4.80421398252924334225227776.1	x^18 + 10x^16 + 32x^14 + 20x^12 - 86x^10 - 172x^8 - 101x^6 - 6x^4 + 8x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 53^{6} \)	18T366	Trivial
18.4.80421398252924334225227776.2	x^18 + 7x^16 + 3x^14 - 46x^12 - 67x^10 + 41x^8 + 130x^6 + 80x^4 + 17x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 53^{6} \)	18T366	$[2]$
18.8.80421398252924334225227776.5	x^18 - 7x^16 - 2x^14 + 59x^12 + 13x^10 - 123x^8 - 87x^6 + 6x^4 + 12x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 53^{6} \)	18T366	Trivial (GRH)
18.8.80421398252924334225227776.6	x^18 + 8x^16 + 4x^14 - 57x^12 - 25x^10 + 133x^8 - 41x^6 - 36x^4 + 13x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 53^{6} \)	18T366	Trivial (GRH)
18.14.279992823820843547402730217.1	x^18 - 6x^17 - 4x^16 + 77x^15 - 52x^14 - 304x^13 + 41x^12 + 1055x^11 + 920x^10 - 4170x^9 - 989x^8 + 6739x^7 + 269x^6 - 4968x^5 - 740x^4 + 1489x^3 + 562x^2 + 24x - 8	\( 7^{12}\cdot 53^{6}\cdot 97^{3} \)	18T366	Trivial (GRH)
18.6.279992823820843547402730217.2	x^18 - 2x^17 + 7x^16 - 31x^15 + 78x^14 - 167x^13 + 228x^12 - 356x^11 - 114x^10 + 1148x^9 - 855x^8 + 1286x^7 - 1036x^6 + 389x^5 + 204x^4 + 43x^3 + 52x^2 + 7x - 1	\( 7^{12}\cdot 53^{6}\cdot 97^{3} \)	18T366	Trivial (GRH)
18.10.279992823820843547402730217.4	x^18 - 3x^17 - 7x^16 + 48x^15 - 117x^14 + 60x^13 + 305x^12 - 712x^11 + 1009x^10 - 302x^9 - 1169x^8 + 2277x^7 - 2584x^6 + 1380x^5 + 119x^4 - 572x^3 - 70x^2 + 8x + 1	\( 7^{12}\cdot 53^{6}\cdot 97^{3} \)	18T366	Trivial (GRH)
18.10.279992823820843547402730217.5	x^18 - 2x^17 - 5x^16 + 2x^15 - 26x^14 + 162x^13 - 11x^12 - 685x^11 + 1063x^10 - 52x^9 - 1788x^8 + 3171x^7 + 3000x^6 - 1295x^5 - 4614x^4 - 1089x^3 + 253x^2 + 4x - 1	\( 7^{12}\cdot 53^{6}\cdot 97^{3} \)	18T366	Trivial (GRH)
18.14.23969878594169966578599985152.1	x^18 - 9x^16 - 12x^14 + 264x^12 - 522x^10 - 360x^8 + 1461x^6 - 747x^4 + 90x^2 - 3	\( 2^{18}\cdot 3^{31}\cdot 23^{6} \)	18T366	Trivial (GRH)
18.6.23969878594169966578599985152.4	x^18 + 9x^16 + 15x^14 - 69x^12 - 216x^10 + 27x^8 + 516x^6 + 324x^4 - 36x^2 - 3	\( 2^{18}\cdot 3^{31}\cdot 23^{6} \)	18T366	Trivial (GRH)
18.0.8984582268650429123395584000000.1	x^18 + 45x^16 + 765x^14 + 6642x^12 + 33048x^10 + 99063x^8 + 180225x^6 + 191889x^4 + 107406x^2 + 23409	\( -\,2^{30}\cdot 3^{32}\cdot 5^{6}\cdot 17^{2} \)	18T366	$[2, 240]$ (GRH)
18.0.26953746805951287370186752000000.1	x^18 + 24x^16 + 243x^14 + 1359x^12 + 4617x^10 + 9864x^8 + 13230x^6 + 10719x^4 + 4743x^2 + 867	\( -\,2^{30}\cdot 3^{33}\cdot 5^{6}\cdot 17^{2} \)	18T366	$[2, 2, 340]$ (GRH)
18.18.26953746805951287370186752000000.1	x^18 - 24x^16 + 243x^14 - 1359x^12 + 4617x^10 - 9864x^8 + 13230x^6 - 10719x^4 + 4743x^2 - 867	\( 2^{30}\cdot 3^{33}\cdot 5^{6}\cdot 17^{2} \)	18T366	Trivial (GRH)
18.18.476878062497693794553036377686016.1	x^18 - 83x^16 + 2799x^14 - 49671x^12 + 503579x^10 - 2976354x^8 + 10074991x^6 - 18519739x^4 + 16871915x^2 - 5929741	\( 2^{18}\cdot 7^{12}\cdot 53^{6}\cdot 181^{3} \)	18T366	Trivial (GRH)
18.10.1459322730319966665579569834938368.1	x^18 - 207x^14 - 186x^12 + 11448x^10 + 5094x^8 - 169566x^6 + 204633x^4 + 101124x^2 - 148877	\( 2^{12}\cdot 3^{38}\cdot 11^{6}\cdot 53^{3} \)	18T366	Trivial (GRH)
18.10.1981841248485867753613659602681856.1	x^18 - 18x^16 - 99x^14 + 2481x^12 + 117x^10 - 81936x^8 + 161004x^6 + 27360x^4 - 35739x^2 - 6859	\( 2^{18}\cdot 3^{32}\cdot 19^{3}\cdot 29^{6} \)	18T366	Trivial (GRH)
18.12.5663571267260801613824000000000000.1	x^18 - 33x^16 + 373x^14 - 1464x^12 - 1954x^10 + 24857x^8 - 25717x^6 - 64003x^4 + 8410x^2 + 24389	\( -\,2^{36}\cdot 5^{12}\cdot 7^{12}\cdot 29^{3} \)	18T366	Trivial (GRH)
18.12.5663571267260801613824000000000000.2	x^18 + 5x^16 - 137x^14 - 188x^12 + 6048x^10 - 8451x^8 - 54601x^6 + 137257x^4 - 102602x^2 + 24389	\( -\,2^{36}\cdot 5^{12}\cdot 7^{12}\cdot 29^{3} \)	18T366	$[2]$ (GRH)
18.8.195977188797288322153846057926340608.1	x^18 - 63x^16 - 249x^15 - 873x^14 + 5403x^13 + 53031x^12 + 207387x^11 + 230385x^10 - 1174006x^9 - 7474338x^8 - 20503479x^7 - 32868075x^6 - 33240231x^5 + 2811813x^4 + 35668848x^3 + 63884925x^2 + 33278943x + 3707657	\( -\,2^{12}\cdot 3^{30}\cdot 7^{6}\cdot 12547^{3} \)	18T366	Trivial (GRH)
18.8.195977188797288322153846057926340608.2	x^18 - 3x^17 + 39x^16 + 81x^15 - 1377x^14 + 12393x^13 - 36342x^12 - 22953x^11 + 783678x^10 - 4048559x^9 + 9075627x^8 + 1377153x^7 - 82704276x^6 + 322084668x^5 - 743501424x^4 + 1159443999x^3 - 1160177862x^2 + 637697091x - 141570217	\( -\,2^{12}\cdot 3^{30}\cdot 7^{6}\cdot 12547^{3} \)	18T366	Trivial (GRH)