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 all 18 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.2.215974961031007317493.1	x^18 + 6x^16 - 7x^15 + 15x^14 - 35x^13 + 39x^12 - 70x^11 + 91x^10 - 95x^9 + 120x^8 - 110x^7 + 92x^6 - 82x^5 + 49x^4 - 28x^3 + 15x^2 - 3x + 1	\( 257^{6}\cdot 749557 \)	18T930	Trivial
18.4.374771407857336924766208.1	x^18 - 12x^16 - 6x^15 + 61x^14 + 60x^13 - 153x^12 - 244x^11 + 144x^10 + 484x^9 + 142x^8 - 408x^7 - 410x^6 - 20x^5 + 204x^4 + 162x^3 + 61x^2 + 12x + 1	\( -\,2^{18}\cdot 23^{6}\cdot 9657384263 \)	18T930	Trivial (GRH)
18.6.15127103235197611307958272.1	x^18 - 18x^16 - 6x^15 + 136x^14 + 90x^13 - 537x^12 - 544x^11 + 1089x^10 + 1636x^9 - 750x^8 - 2358x^7 - 832x^6 + 1022x^5 + 1179x^4 + 546x^3 + 136x^2 + 18x + 1	\( 2^{18}\cdot 23^{6}\cdot 109\cdot 3576204413 \)	18T930	Trivial (GRH)
18.12.627404582148122400842842112.1	x^18 - 12x^16 - 6x^15 + 54x^14 + 60x^13 - 97x^12 - 216x^11 - 17x^10 + 316x^9 + 296x^8 - 86x^7 - 326x^6 - 188x^5 + 43x^4 + 106x^3 + 54x^2 + 12x + 1	\( -\,2^{18}\cdot 257^{6}\cdot 1789\cdot 4643 \)	18T930	Trivial (GRH)
18.4.2193332822441279165533519872.1	x^18 - 18x^16 - 6x^15 + 135x^14 + 90x^13 - 576x^12 - 540x^11 + 1647x^10 + 1920x^9 - 3402x^8 - 5130x^7 + 5693x^6 + 9558x^5 - 9372x^4 - 7140x^3 + 9684x^2 - 2880x + 272	\( -\,2^{27}\cdot 3^{18}\cdot 59^{6} \)	18T930	Trivial (GRH)
18.8.6845608158779552856188649472.1	x^18 - 6x^15 - 6x^14 + 15x^12 + 24x^11 + 8x^10 - 20x^9 - 36x^8 - 16x^7 + 14x^6 + 24x^5 + 8x^4 - 6x^3 - 6x^2 + 1	\( -\,2^{18}\cdot 229^{6}\cdot 1657\cdot 109279 \)	18T930	Trivial (GRH)
18.10.26979277591675021288064417792.1	x^18 - 6x^16 - 6x^15 + 9x^14 + 30x^13 + 19x^12 - 36x^11 - 73x^10 - 32x^9 + 56x^8 + 86x^7 + 29x^6 - 38x^5 - 43x^4 - 10x^3 + 9x^2 + 6x + 1	\( 2^{18}\cdot 229^{6}\cdot 713637233 \)	18T930	Trivial (GRH)
18.16.70102248494107553872773644288.1	x^18 - 24x^16 - 6x^15 + 234x^14 + 120x^13 - 1169x^12 - 936x^11 + 3031x^10 + 3532x^9 - 3260x^8 - 6302x^7 - 866x^6 + 3728x^5 + 3151x^4 + 1178x^3 + 234x^2 + 24x + 1	\( -\,2^{18}\cdot 127\cdot 257^{6}\cdot 7307849 \)	18T930	Trivial (GRH)
18.2.1052719060501925259206838976512.1	x^18 - 18x^16 - 12x^15 + 117x^14 + 156x^13 - 196x^12 - 432x^11 - 264x^10 - 1344x^9 - 504x^8 + 4752x^7 + 6180x^6 + 3600x^5 + 10128x^4 - 1408x^3 - 5760x^2 + 1536x + 512	\( 2^{49}\cdot 3^{18}\cdot 13^{6} \)	18T930	Trivial (GRH)
18.14.2789809332532465693606115803136.1	x^18 - 18x^16 - 6x^15 + 129x^14 + 90x^13 - 453x^12 - 516x^11 + 718x^10 + 1384x^9 - 78x^8 - 1616x^7 - 1084x^6 + 336x^5 + 808x^4 + 462x^3 + 129x^2 + 18x + 1	\( 2^{18}\cdot 101\cdot 257^{6}\cdot 365691181 \)	18T930	Trivial (GRH)
18.8.14998069355851395963169290584064.1	x^18 - 72x^14 - 96x^13 - 194x^12 - 108x^11 + 240x^10 + 2784x^9 + 648x^8 + 1680x^7 + 3201x^6 - 2988x^5 - 1128x^4 - 3072x^3 - 2304x^2 + 1536x - 64	\( -\,2^{28}\cdot 3^{18}\cdot 229^{6} \)	18T930	Trivial (GRH)
18.2.51774386757903605816150691151872.1	x^18 - 6x^16 - 32x^15 - 63x^14 + 216x^13 + 576x^12 + 648x^11 + 828x^10 - 6096x^9 - 13248x^8 + 6096x^7 + 24388x^6 + 3168x^5 - 17328x^4 - 4992x^3 + 4608x^2 - 1536x - 512	\( 2^{39}\cdot 3^{18}\cdot 79^{6} \)	18T930	Trivial (GRH)
18.18.169603511485311035374422125182976.1	x^18 - 24x^16 - 6x^15 + 234x^14 + 120x^13 - 1169x^12 - 936x^11 + 3032x^10 + 3532x^9 - 3268x^8 - 6304x^7 - 850x^6 + 3736x^5 + 3152x^4 + 1178x^3 + 234x^2 + 24x + 1	\( 2^{18}\cdot 229^{6}\cdot 4486235045849 \)	18T930	Trivial (GRH)
18.6.586199654891248362767163209023488.1	x^18 - 18x^16 - 12x^15 + 45x^14 + 60x^13 - 94x^12 + 756x^11 - 978x^10 - 1200x^9 - 540x^8 - 2280x^7 + 3305x^6 + 7812x^5 + 4608x^4 - 7360x^3 - 2880x^2 + 5376x - 512	\( 2^{24}\cdot 3^{18}\cdot 257^{6}\cdot 313 \)	18T930	Trivial (GRH)
18.4.94905995402807932797658494211719168.1	x^18 + 24x^16 - 16x^15 + 144x^14 - 192x^13 - 206x^12 + 756x^11 - 4872x^10 + 12096x^9 - 20160x^8 + 16128x^7 - 847x^6 - 79380x^5 + 188160x^4 - 228928x^3 + 112896x^2 - 21952	\( -\,2^{26}\cdot 3^{18}\cdot 7^{9}\cdot 67^{6} \)	18T930	$[2]$ (GRH)
18.16.86460885220681483299874289528302731264.1	x^18 - 102x^16 - 68x^15 + 3987x^14 + 5316x^13 - 76498x^12 - 151956x^11 + 739557x^10 + 2038344x^9 - 3005856x^8 - 13120632x^7 - 852796x^6 + 34623792x^5 + 30096192x^4 - 16376192x^3 - 22127616x^2 + 614656	\( -\,2^{28}\cdot 3^{18}\cdot 7^{8}\cdot 229^{6} \)	18T930	Trivial (GRH)
18.18.482171486214841046540312290712431689203712.1	x^18 - 162x^16 - 108x^15 + 10071x^14 + 13428x^13 - 311714x^12 - 611604x^11 + 5070909x^10 + 13203576x^9 - 40277844x^8 - 140567976x^7 + 100691908x^6 + 660320208x^5 + 295462464x^4 - 833087232x^3 - 729925632x^2 + 81102848	\( 2^{27}\cdot 3^{18}\cdot 41\cdot 199^{4}\cdot 229^{6} \)	18T930	Trivial (GRH)
18.6.140250563298174994466424880921916297888335707242496.1	x^18 - 6x^16 - 136x^15 - 35001x^14 + 119340x^13 + 957484x^12 - 202896x^11 + 233675115x^10 - 2033502752x^9 + 272513106x^8 + 55913318808x^7 - 253258909175x^6 + 18048051900x^5 + 2492339844720x^4 - 5055629947608x^3 - 2688635549088x^2 + 20583488547936x - 20669191866896	\( 2^{34}\cdot 3^{24}\cdot 13\cdot 37^{7}\cdot 89^{4}\cdot 139^{4} \)	18T930	$[3, 3]$ (GRH)