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 93728)

Label	Polynomial	Discriminant	Galois group	Class group
18.0.10490638424730354432.1	x^18 - 4x^17 + 11x^16 - 20x^15 + 31x^14 - 41x^13 + 56x^12 - 69x^11 + 64x^10 - 59x^9 + 49x^8 - 48x^7 + 28x^6 - 5x^5 + 17x^4 - 5x^3 - 2x^2 - x + 1	\( -\,2^{8}\cdot 3^{9}\cdot 113^{6} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial
18.0.167850214795685670912.1	x^18 - 7x^15 + 12x^12 + 13x^9 + 12x^6 - 7x^3 + 1	\( -\,2^{12}\cdot 3^{9}\cdot 113^{6} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial
18.6.399097135460205078125.1	x^18 - x^17 - 6x^16 + 9x^15 + 11x^14 - 29x^13 - 2x^12 + 66x^11 - 31x^10 - 123x^9 + 77x^8 + 156x^7 - 78x^6 - 117x^5 + 29x^4 + 41x^3 - 3x - 1	\( 5^{13}\cdot 83^{6} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial
18.6.1937102445000000000000.1	x^18 - 6x^17 + 15x^16 - 34x^15 + 93x^14 - 168x^13 + 166x^12 - 132x^11 + 102x^10 + 62x^9 - 201x^8 + 138x^7 - 83x^6 + 24x^5 + 51x^4 - 4x^3 - 30x^2 + 6x + 1	\( 2^{12}\cdot 3^{18}\cdot 5^{13} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial
18.0.2538998916710400000000.1	x^18 + 3x^16 - 3x^14 - 16x^12 - 24x^10 + 15x^8 + 51x^6 + 63x^4 + 18x^2 + 1	\( -\,2^{24}\cdot 3^{18}\cdot 5^{8} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial
18.6.3026722570312500000000.1	x^18 - 3x^17 - 3x^16 + 17x^15 - 48x^13 + 29x^12 + 54x^11 - 66x^10 - 5x^9 + 72x^8 + 9x^7 - 201x^6 + 174x^5 - 78x^3 + 84x^2 - 36x + 4	\( 2^{8}\cdot 3^{18}\cdot 5^{15} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial
18.6.9977428386505126953125.1	x^18 - 5x^17 + 11x^16 - 16x^15 + 10x^14 + 25x^13 - 125x^12 + 390x^11 - 830x^10 + 1150x^9 - 969x^8 + 245x^7 + 536x^6 - 741x^5 + 395x^4 - 71x^3 - 5x^2 - x + 1	\( 5^{15}\cdot 83^{6} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial
18.0.52301766015000000000000.1	x^18 + 9x^16 - x^15 + 27x^14 - 6x^13 + 46x^12 - 27x^11 + 123x^10 - 83x^9 + 234x^8 - 54x^7 + 118x^6 + 48x^5 + 132x^4 + 108x^3 + 336x^2 + 264x + 184	\( -\,2^{12}\cdot 3^{21}\cdot 5^{13} \)	$C_2\times C_3^2:S_3$ (as 18T52)	$[2]$
18.6.68552970751180800000000.1	x^18 - 18x^15 - 15x^14 - 12x^13 + 45x^12 + 138x^11 + 123x^10 - 34x^9 - 126x^8 - 90x^7 - 144x^6 - 132x^5 - 57x^4 - 18x^3 - 15x^2 + 6x + 1	\( 2^{24}\cdot 3^{21}\cdot 5^{8} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial (GRH)
18.0.81721509398437500000000.1	x^18 - 6x^17 + 18x^16 - 34x^15 + 45x^14 - 66x^13 + 176x^12 - 498x^11 + 1104x^10 - 1890x^9 + 2523x^8 - 2628x^7 + 2139x^6 - 1362x^5 + 675x^4 - 254x^3 + 69x^2 - 12x + 1	\( -\,2^{8}\cdot 3^{21}\cdot 5^{15} \)	$C_2\times C_3^2:S_3$ (as 18T52)	$[2]$
18.0.396718580736000000000000.1	x^18 + 3x^16 - 3x^14 - 13x^12 + 27x^10 + 108x^8 + 78x^6 - 15x^4 - 6x^2 + 1	\( -\,2^{22}\cdot 3^{18}\cdot 5^{12} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial
18.0.1299967445355724800000000.1	x^18 - 12x^14 + 4x^12 + 12x^10 + 144x^8 - 300x^6 + 72x^4 + 96x^2 + 8	\( -\,2^{33}\cdot 3^{18}\cdot 5^{8} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial
18.6.1299967445355724800000000.1	x^18 - 12x^14 - 4x^12 + 12x^10 - 144x^8 - 300x^6 - 72x^4 + 96x^2 - 8	\( 2^{33}\cdot 3^{18}\cdot 5^{8} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial (GRH)
18.0.1393297834614409075359744.1	x^18 + 3x^16 - 15x^14 - 24x^12 + 180x^10 + 219x^8 - 649x^6 - 561x^4 + 750x^2 + 625	\( -\,2^{24}\cdot 3^{18}\cdot 11^{8} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial
18.6.3922632451125000000000000.1	x^18 - 9x^17 + 38x^16 - 99x^15 + 160x^14 - 134x^13 - 4x^12 + 223x^11 - 549x^10 + 805x^9 - 832x^8 + 713x^7 - 536x^6 + 413x^5 - 195x^4 + 151x^3 - 59x^2 - 7x + 1	\( 2^{12}\cdot 3^{22}\cdot 5^{15} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial (GRH)
18.6.3922632451125000000000000.2	x^18 - 3x^16 - 6x^15 - 20x^14 + 10x^13 + 55x^12 - 63x^8 + 720x^7 + 189x^6 - 1062x^5 + 180x^4 + 504x^3 - 180x^2 - 72x + 36	\( 2^{12}\cdot 3^{22}\cdot 5^{15} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial (GRH)
18.6.3922632451125000000000000.3	x^18 - 3x^16 - 18x^15 - 20x^14 + 65x^13 + 160x^12 + 60x^11 - 420x^10 - 795x^9 + 507x^8 + 2490x^7 + 39x^6 - 3771x^5 - 1035x^4 + 2277x^3 + 900x^2 - 171x + 9	\( 2^{12}\cdot 3^{22}\cdot 5^{15} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial (GRH)
18.0.7934371614720000000000000.1	x^18 - 28x^15 + 12x^14 + 48x^13 + 224x^12 - 264x^11 - 252x^10 - 620x^9 + 1128x^8 + 240x^7 + 2020x^6 - 3264x^5 - 264x^4 - 616x^3 + 1512x^2 + 288x + 344	\( -\,2^{24}\cdot 3^{18}\cdot 5^{13} \)	$C_2\times C_3^2:S_3$ (as 18T52)	$[2]$ (GRH)
18.6.10711401679872000000000000.1	x^18 - 9x^16 + 33x^14 - 117x^12 - 45x^10 + 72x^8 + 18x^6 - 27x^4 + 54x^2 - 27	\( 2^{22}\cdot 3^{21}\cdot 5^{12} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial (GRH)
18.6.19533453031125000000000000.1	x^18 - 4x^17 + 6x^16 + x^15 - 50x^14 + 156x^13 - 204x^12 - 24x^11 + 836x^10 - 1955x^9 + 1926x^8 + 136x^7 - 3924x^6 + 7046x^5 - 6140x^4 + 3221x^3 - 504x^2 - 584x - 449	\( 2^{12}\cdot 3^{6}\cdot 5^{15}\cdot 11^{8} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial (GRH)
18.0.22663531051370805643444224.2	x^18 + 18x^16 + 135x^14 + 555x^12 + 1395x^10 + 2268x^8 + 2424x^6 + 1665x^4 + 675x^2 + 121	\( -\,2^{24}\cdot 3^{38} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial
18.0.22663531051370805643444224.3	x^18 + 18x^16 + 135x^14 + 543x^12 + 1251x^10 + 1620x^8 + 1068x^6 + 333x^4 + 135x^2 + 1	\( -\,2^{24}\cdot 3^{38} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial (GRH)
18.0.22663531051370805643444224.4	x^18 + 18x^16 + 135x^14 + 540x^12 + 1215x^10 + 1458x^8 + 729x^6 + 16	\( -\,2^{24}\cdot 3^{38} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial (GRH)
18.0.25014102650966116800000000.1	x^18 - 3x^17 + 9x^16 - 8x^15 + 9x^13 + 23x^12 - 129x^11 + 456x^10 - 635x^9 + 894x^8 - 804x^7 + 2800x^6 - 3456x^5 + 9120x^4 - 6592x^3 + 5760x^2 - 1536x + 512	\( -\,2^{12}\cdot 3^{18}\cdot 5^{8}\cdot 7^{9} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial (GRH)
18.0.35099121024604569600000000.1	x^18 + 12x^16 + 24x^14 + 54x^12 + 36x^10 - 144x^8 + 72x^6 - 216x^4 + 864x^2 + 216	\( -\,2^{33}\cdot 3^{21}\cdot 5^{8} \)	$C_2\times C_3^2:S_3$ (as 18T52)	$[2]$ (GRH)
18.6.35099121024604569600000000.1	x^18 - 12x^16 + 24x^14 - 54x^12 + 36x^10 + 144x^8 + 72x^6 + 216x^4 + 864x^2 - 216	\( 2^{33}\cdot 3^{21}\cdot 5^{8} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial (GRH)
18.6.37619041534589045034713088.1	x^18 - 6x^16 + 3x^14 + 3x^12 + 99x^10 - 252x^8 + 648x^6 - 891x^4 + 891x^2 - 675	\( 2^{24}\cdot 3^{21}\cdot 11^{8} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial (GRH)
18.0.45341287899989790827741184.1	x^18 + 3x^16 - 9x^14 - 51x^12 + 204x^10 - 496x^6 + 2496x^4 + 3840x^2 + 1024	\( -\,2^{24}\cdot 3^{18}\cdot 17^{8} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial (GRH)
18.0.49589822592000000000000000.1	x^18 + 15x^16 + 105x^14 + 475x^12 + 1575x^10 + 3600x^8 + 4650x^6 + 2625x^4 + 750x^2 + 125	\( -\,2^{22}\cdot 3^{18}\cdot 5^{15} \)	$C_2\times C_3^2:S_3$ (as 18T52)	$[2]$ (GRH)
18.0.54783205459591112303652864.2	x^18 - 9x^17 + 42x^16 - 119x^15 + 219x^14 - 219x^13 - 63x^12 + 720x^11 - 1461x^10 + 1613x^9 - 378x^8 - 2184x^7 + 5316x^6 - 7317x^5 + 7290x^4 - 5308x^3 + 2691x^2 - 834x + 125	\( -\,2^{12}\cdot 3^{18}\cdot 11^{13} \)	$C_2\times C_3^2:S_3$ (as 18T52)	$[3]$ (GRH)
18.6.64340978779577812500000000.1	x^18 - 3x^17 + 12x^16 - 19x^15 - 33x^14 + 120x^13 - 276x^12 + 516x^11 - 948x^10 + 806x^9 - 2505x^8 + 3867x^7 - 2377x^6 + 2646x^5 - 72x^4 - 642x^3 - 108x^2 + 36	\( 2^{8}\cdot 3^{30}\cdot 5^{13} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial (GRH)
18.6.67990593154112416930332672.1	x^18 - 18x^16 + 135x^14 - 552x^12 + 1359x^10 - 2106x^8 + 2073x^6 - 1260x^4 + 432x^2 - 48	\( 2^{24}\cdot 3^{39} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial (GRH)
18.6.67990593154112416930332672.2	x^18 - 18x^16 + 135x^14 - 549x^12 + 1323x^10 - 1944x^8 + 1740x^6 - 963x^4 + 351x^2 - 75	\( 2^{24}\cdot 3^{39} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial (GRH)
18.6.67990593154112416930332672.5	x^18 - 18x^16 + 135x^14 - 537x^12 + 1179x^10 - 1296x^8 + 408x^6 + 225x^4 + 27x^2 - 3	\( 2^{24}\cdot 3^{39} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial (GRH)
18.0.105911076180375000000000000.1	x^18 + x^16 - 9x^15 - 5x^14 + 180x^12 + 255x^11 + 1065x^10 - 45x^9 + 1866x^8 - 3150x^7 + 2106x^6 - 4464x^5 + 4680x^4 + 216x^3 - 1800x^2 + 216x + 216	\( -\,2^{12}\cdot 3^{25}\cdot 5^{15} \)	$C_2\times C_3^2:S_3$ (as 18T52)	$[2]$ (GRH)
18.0.105911076180375000000000000.2	x^18 - 7x^17 + 24x^16 - 52x^15 + 90x^14 - 122x^13 + 204x^12 - 388x^11 + 1049x^10 - 2415x^9 + 5604x^8 - 10288x^7 + 16596x^6 - 20168x^5 + 21040x^4 - 15392x^3 + 9344x^2 - 2048x + 1024	\( -\,2^{12}\cdot 3^{25}\cdot 5^{15} \)	$C_2\times C_3^2:S_3$ (as 18T52)	$[2]$ (GRH)
18.0.105911076180375000000000000.4	x^18 - 7x^17 + 24x^16 - 58x^15 + 135x^14 - 287x^13 + 534x^12 - 1003x^11 + 1976x^10 - 3285x^9 + 4584x^8 - 5713x^7 + 5976x^6 - 5117x^5 + 3655x^4 - 1688x^3 + 1316x^2 - 1127x + 349	\( -\,2^{12}\cdot 3^{25}\cdot 5^{15} \)	$C_2\times C_3^2:S_3$ (as 18T52)	$[2]$ (GRH)
18.0.128536820158464000000000000.1	x^18 - 6x^15 - 32x^14 - 24x^13 + 18x^12 - 12x^11 - 36x^10 + 180x^9 + 936x^8 + 2592x^7 + 5328x^6 + 8568x^5 + 10800x^4 + 10368x^3 + 7056x^2 + 3024x + 648	\( -\,2^{24}\cdot 3^{22}\cdot 5^{12} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial (GRH)
18.0.128536820158464000000000000.2	x^18 + 10x^16 + 47x^14 + 195x^12 - 97x^10 + 100x^8 - 636x^6 + 85x^4 + 275x^2 + 25	\( -\,2^{24}\cdot 3^{22}\cdot 5^{12} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial (GRH)
18.0.128536820158464000000000000.3	x^18 - 2x^17 + 2x^16 - 18x^15 + 60x^14 - 120x^13 + 282x^12 - 692x^11 + 1220x^10 - 2192x^9 + 4680x^8 - 7056x^7 + 8592x^6 - 11776x^5 + 11008x^4 - 5376x^3 + 4096x^2 - 4096x + 2048	\( -\,2^{24}\cdot 3^{22}\cdot 5^{12} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial (GRH)
18.0.203119913336832000000000000.1	x^18 + 18x^16 + 96x^14 + 166x^12 + 204x^10 + 360x^8 - 284x^6 + 336x^4 - 48x^2 + 32	\( -\,2^{31}\cdot 3^{18}\cdot 5^{12} \)	$C_2\times C_3^2:S_3$ (as 18T52)	$[3]$ (GRH)
18.6.203119913336832000000000000.1	x^18 - 18x^16 + 96x^14 - 166x^12 + 204x^10 - 360x^8 - 284x^6 - 336x^4 - 48x^2 - 32	\( 2^{31}\cdot 3^{18}\cdot 5^{12} \)	$C_2\times C_3^2:S_3$ (as 18T52)	$[2]$ (GRH)
18.6.214228033597440000000000000.1	x^18 - 32x^15 + 27x^14 + 162x^13 + 39x^12 - 1656x^11 + 1293x^10 + 5640x^9 - 6792x^8 - 11010x^7 + 20030x^6 + 10854x^5 - 30129x^4 + 1826x^3 + 7347x^2 - 5988x + 5569	\( 2^{24}\cdot 3^{21}\cdot 5^{13} \)	$C_2\times C_3^2:S_3$ (as 18T52)	$[2]$ (GRH)
18.6.317733228541125000000000000.1	x^18 - 3x^16 - 6x^15 - 125x^12 - 270x^11 - 180x^10 - 60x^9 - 333x^8 - 90x^7 + 1539x^6 + 2268x^5 + 990x^4 - 36x^3 + 108x + 36	\( 2^{12}\cdot 3^{26}\cdot 5^{15} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial (GRH)
18.6.317733228541125000000000000.3	x^18 - 3x^16 - 12x^15 + 45x^13 - 80x^12 - 180x^10 + 285x^9 - 333x^8 + 270x^7 + 459x^6 - 459x^5 + 585x^4 - 477x^3 + 81x + 9	\( 2^{12}\cdot 3^{26}\cdot 5^{15} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial (GRH)
18.0.337332030823872921600000000.1	x^18 + 9x^16 + 18x^14 + 177x^12 + 1008x^10 + 2592x^8 + 3888x^6 + 3456x^4 + 2304x^2 + 256	\( -\,2^{22}\cdot 3^{30}\cdot 5^{8} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial (GRH)
18.0.414297991288157786796374784.1	x^18 - 9x^17 + 42x^16 - 119x^15 + 192x^14 - 138x^13 - 13x^12 - 216x^11 + 1170x^10 - 1803x^9 + 771x^8 + 1359x^7 - 1597x^6 + 228x^5 + 918x^4 - 314x^3 - 156x^2 + 132x + 92	\( -\,2^{8}\cdot 3^{18}\cdot 11^{15} \)	$C_2\times C_3^2:S_3$ (as 18T52)	$[2]$ (GRH)
18.0.458936503790258814279745536.1	x^18 + 18x^16 + 81x^14 + 210x^12 + 360x^10 + 567x^8 + 579x^6 + 153x^4 + 27x^2 + 1	\( -\,2^{22}\cdot 3^{42} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial (GRH)
18.0.458936503790258814279745536.2	x^18 + 18x^16 + 117x^14 + 306x^12 + 108x^10 - 729x^8 - 405x^6 + 945x^4 - 81x^2 + 225	\( -\,2^{22}\cdot 3^{42} \)	$C_2\times C_3^2:S_3$ (as 18T52)	Trivial (GRH)
18.0.509008657395156683109433344.1	x^18 + 18x^16 + 111x^14 + 375x^12 + 795x^10 + 1092x^8 + 824x^6 + 213x^4 + 27x^2 + 1	\( -\,2^{24}\cdot 3^{18}\cdot 23^{8} \)	$C_2\times C_3^2:S_3$ (as 18T52)	$[3]$ (GRH)