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 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.8.395754347757959764770816.3	x^18 - 6x^16 + 9x^14 - 11x^12 + 33x^10 - 36x^8 + 14x^6 + 69x^4 - 21x^2 + 1	\( -\,2^{24}\cdot 3^{24}\cdot 17^{4} \)	18T705	Trivial (GRH)
18.8.395754347757959764770816.4	x^18 - 6x^16 - 6x^14 + 29x^12 + 21x^10 - 45x^8 - 17x^6 + 30x^4 - 9x^2 + 1	\( -\,2^{24}\cdot 3^{24}\cdot 17^{4} \)	18T705	Trivial (GRH)
18.4.395754347757959764770816.5	x^18 + 6x^16 + 12x^14 - x^12 - 45x^10 - 81x^8 - 75x^6 - 42x^4 - 9x^2 + 1	\( -\,2^{24}\cdot 3^{24}\cdot 17^{4} \)	18T705	Trivial (GRH)
18.4.656193316976757965848576.1	x^18 + 10x^16 + 37x^14 + 53x^12 + 21x^10 - 96x^8 - 162x^6 - 51x^4 + 19x^2 + 1	\( -\,2^{24}\cdot 7^{12}\cdot 41^{4} \)	18T705	Trivial (GRH)
18.2.3056899980033856376345653.1	x^18 - 7x^17 + 21x^16 - 22x^15 - 37x^14 + 165x^13 - 227x^12 + 20x^11 + 498x^10 - 958x^9 + 722x^8 + 345x^7 - 1229x^6 + 838x^5 + 133x^4 - 298x^3 - 9x^2 + 16x + 29	\( 7^{12}\cdot 13^{5}\cdot 29^{6} \)	18T705	Trivial (GRH)
18.2.3056899980033856376345653.2	x^18 - 5x^17 + 11x^16 - 20x^15 + 34x^14 - 42x^13 + 51x^12 - 89x^11 + 167x^10 - 269x^9 + 397x^8 - 550x^7 + 552x^6 - 467x^5 + 393x^4 - 168x^3 + 60x^2 - 13	\( 7^{12}\cdot 13^{5}\cdot 29^{6} \)	18T705	Trivial (GRH)
18.6.5249546535814063726788608.1	x^18 - 17x^14 - 55x^12 + 164x^10 + 26x^8 - 248x^6 + 120x^4 + 16x^2 - 8	\( 2^{27}\cdot 7^{12}\cdot 41^{4} \)	18T705	Trivial (GRH)
18.6.10685367389464913648812032.2	x^18 - 9x^14 + 117x^12 - 333x^10 - 216x^8 + 1206x^6 - 945x^4 + 243x^2 - 27	\( 2^{24}\cdot 3^{27}\cdot 17^{4} \)	18T705	Trivial (GRH)
18.6.127609123015304468465889942421.1	x^18 - 6x^17 + 15x^16 - 18x^15 - 33x^14 + 175x^13 - 473x^12 + 1035x^11 - 1455x^10 + 1697x^9 - 1438x^8 + 652x^7 + 167x^6 - 916x^5 + 1495x^4 - 1079x^3 + 728x^2 - 133x + 7	\( 7^{12}\cdot 83^{4}\cdot 181^{5} \)	18T705	Trivial (GRH)
18.6.127609123015304468465889942421.2	x^18 - 3x^17 + 8x^16 - 27x^15 + 4x^14 - 14x^13 - 186x^12 + 402x^11 - 287x^10 + 590x^9 + 2167x^8 + 1649x^7 + 3794x^6 + 3188x^5 + 8373x^4 + 7097x^3 + 3356x^2 + 4530x + 1429	\( 7^{12}\cdot 83^{4}\cdot 181^{5} \)	18T705	Trivial (GRH)
18.10.127609123015304468465889942421.3	x^18 - 3x^17 - 19x^16 + 45x^15 + 103x^14 - 105x^13 - 70x^12 - 495x^11 - 885x^10 + 370x^9 + 1266x^8 + 4890x^7 + 2947x^6 + 1645x^5 - 1663x^4 - 9393x^3 - 4060x^2 - 3486x + 7441	\( 7^{12}\cdot 83^{4}\cdot 181^{5} \)	18T705	Trivial (GRH)
18.10.127609123015304468465889942421.4	x^18 - 2x^17 - 9x^16 - 26x^15 + 70x^14 + 304x^13 - 40x^12 - 744x^11 - 891x^10 + 2419x^9 + 5641x^8 - 6035x^7 - 8603x^6 + 12006x^5 + 6765x^4 - 8900x^3 - 2424x^2 + 1740x + 491	\( 7^{12}\cdot 83^{4}\cdot 181^{5} \)	18T705	Trivial (GRH)
18.4.893263861107131279261229596947.1	x^18 - 6x^17 + 28x^16 - 99x^15 + 171x^14 - 448x^13 - 196x^12 + 368x^11 - 3644x^10 + 7253x^9 - 5633x^8 + 10750x^7 + 1023x^6 + 3316x^5 - 3548x^4 - 2435x^3 + 858x^2 + 249x - 71	\( -\,7^{13}\cdot 83^{4}\cdot 181^{5} \)	18T705	$[2]$ (GRH)
18.8.893263861107131279261229596947.1	x^18 + 7x^16 - 62x^14 - 434x^12 + 733x^10 + 6209x^8 + 2988x^6 - 7770x^4 - 4200x^2 + 1267	\( -\,7^{13}\cdot 83^{4}\cdot 181^{5} \)	18T705	Trivial (GRH)
18.12.893263861107131279261229596947.2	x^18 - 6x^17 + x^16 + 68x^15 - 170x^14 - 135x^13 + 1436x^12 - 1169x^11 - 6090x^10 + 7265x^9 + 18146x^8 - 19423x^7 - 38155x^6 + 32920x^5 + 41054x^4 - 30150x^3 - 12208x^2 + 5929x + 343	\( -\,7^{13}\cdot 83^{4}\cdot 181^{5} \)	18T705	Trivial (GRH)
18.8.893263861107131279261229596947.2	x^18 - 5x^17 - 11x^16 + 101x^15 - 108x^14 - 447x^13 + 1410x^12 - 1217x^11 - 1460x^10 + 4952x^9 - 9778x^8 + 21755x^7 - 22089x^6 - 11191x^5 + 39039x^4 - 34564x^3 + 13883x^2 - 1575x - 377	\( -\,7^{13}\cdot 83^{4}\cdot 181^{5} \)	18T705	Trivial (GRH)
18.12.893263861107131279261229596947.3	x^18 - x^17 - 18x^16 - 12x^15 + 265x^14 + 387x^13 - 2448x^12 - 4826x^11 + 12112x^10 + 29015x^9 - 31282x^8 - 77255x^7 + 43356x^6 + 90316x^5 - 29861x^4 - 43358x^3 + 8768x^2 + 6731x - 1079	\( -\,7^{13}\cdot 83^{4}\cdot 181^{5} \)	18T705	Trivial (GRH)
18.14.6252847027749918954828607178629.1	x^18 - 6x^17 - 20x^16 + 178x^15 - 42x^14 - 1645x^13 + 2472x^12 + 6027x^11 - 17526x^10 - 4004x^9 + 55119x^8 - 33512x^7 - 83181x^6 + 100613x^5 + 46791x^4 - 111650x^3 + 12449x^2 + 43838x - 16393	\( 7^{14}\cdot 83^{4}\cdot 181^{5} \)	18T705	Trivial (GRH)
18.14.879099248452432483261515813338269.1	x^18 - 5x^17 - 25x^16 + 208x^15 - 80x^14 - 2967x^13 + 7770x^12 + 13604x^11 - 86024x^10 + 53003x^9 + 346564x^8 - 680103x^7 - 176218x^6 + 1846244x^5 - 1806627x^4 - 628952x^3 + 2353229x^2 - 1585148x + 344357	\( 7^{12}\cdot 83^{6}\cdot 181^{5} \)	18T705	Trivial (GRH)
18.4.6153694739167027382830610693367883.1	x^18 - 6x^17 + 47x^16 - 360x^15 + 1843x^14 - 9567x^13 + 42845x^12 - 165051x^11 + 553361x^10 - 1580866x^9 + 3726139x^8 - 6574343x^7 + 7643106x^6 - 2574322x^5 - 8647295x^4 + 18580467x^3 - 17157215x^2 + 7576254x - 862709	\( -\,7^{13}\cdot 83^{6}\cdot 181^{5} \)	18T705	$[4]$ (GRH)
18.0.25003618613826788543103612846080000.1	x^18 + 46x^16 + 692x^14 + 4346x^12 + 13828x^10 + 24070x^8 + 23056x^6 + 11386x^4 + 2323x^2 + 47	\( -\,2^{18}\cdot 5^{4}\cdot 13^{16}\cdot 47^{5} \)	18T705	$[4380]$ (GRH)
18.0.325047041979748251060346966999040000.1	x^18 + 65x^16 + 1352x^14 + 13650x^12 + 76596x^10 + 248313x^8 + 454766x^6 + 430820x^4 + 173537x^2 + 15275	\( -\,2^{18}\cdot 5^{4}\cdot 13^{17}\cdot 47^{5} \)	18T705	$[2, 3856]$ (GRH)
18.18.381930274326204194995907686223872000000.1	x^18 - 91x^16 + 3159x^14 - 53677x^12 + 486239x^10 - 2410070x^8 + 6531122x^6 - 9199216x^4 + 5654805x^2 - 717925	\( 2^{18}\cdot 5^{6}\cdot 13^{17}\cdot 47^{6} \)	18T705	$[2]$ (GRH)
18.18.601687078323127839501245339528069120000.1	x^18 - 102x^16 + 3844x^14 - 71296x^12 + 718032x^10 - 4067136x^8 + 12791552x^6 - 20692992x^4 + 13788672x^2 - 1131008	\( 2^{27}\cdot 5^{4}\cdot 13^{16}\cdot 47^{6} \)	18T705	$[2]$ (GRH)