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 12 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.0.12619972448180608967.1	x^18 - 3x^17 + 6x^16 - 7x^15 + 4x^14 + 2x^13 - 4x^12 - 3x^11 + 14x^10 - 19x^9 + 17x^8 - 6x^7 - 10x^6 + 18x^5 - 9x^4 - 6x^3 + 10x^2 - 5x + 1	\( -\,23^{9}\cdot 2647^{2} \)	18T319	Trivial
18.0.14929107797061341783.1	x^18 - x^17 - x^16 + x^15 + 3x^14 + 2x^13 - 5x^12 + 4x^11 + 5x^10 + 5x^9 + 6x^8 - 4x^7 + 8x^6 - 5x^5 + 5x^4 + x^3 + 2x^2 - x + 1	\( -\,23^{9}\cdot 2879^{2} \)	18T319	Trivial
18.0.263576013691949569367.1	x^18 - x^17 - 2x^16 + x^15 + 7x^14 - 15x^13 + 9x^12 + 19x^11 - 28x^10 - 25x^9 + 88x^8 - 66x^7 - 15x^6 + 46x^5 - 5x^4 - 34x^3 + 28x^2 - 8x + 1	\( -\,23^{9}\cdot 12097^{2} \)	18T319	Trivial
18.0.395004451929234841703.1	x^18 - 2x^17 - 2x^16 + 3x^15 + 8x^14 - 6x^13 - 9x^12 + 6x^11 + 28x^10 + 3x^9 + 24x^8 + 25x^7 + 24x^6 + 14x^4 + x^3 + x^2 + x + 1	\( -\,23^{9}\cdot 59^{2}\cdot 251^{2} \)	18T319	Trivial
18.6.12137503248660687572992.1	x^18 - 5x^17 + 7x^16 - 5x^15 + 20x^14 - 40x^13 + 33x^12 - 26x^11 + 31x^10 - 38x^9 - 16x^8 + 82x^7 - 71x^6 + 109x^5 - 144x^4 + 126x^3 - 12x^2 - 40x + 25	\( 2^{12}\cdot 37^{9}\cdot 151^{2} \)	18T319	Trivial
18.10.85598116744348371668992.1	x^18 - 4x^17 + 3x^16 + 14x^15 - 46x^14 + 41x^13 + 72x^12 - 216x^11 + 76x^10 + 273x^9 - 151x^8 - 170x^7 + 53x^6 + 93x^5 - 79x^4 + 45x^3 - 7x + 1	\( 2^{12}\cdot 37^{9}\cdot 401^{2} \)	18T319	Trivial
18.6.97513108859377193648128.1	x^18 - x^17 + 3x^16 - 2x^15 - 2x^14 - 22x^13 - 22x^12 + 4x^11 - 29x^10 + 55x^9 - 57x^8 + 36x^7 - 2x^6 + 8x^5 + 32x^4 - 34x^3 + 9x^2 - 3x + 1	\( 2^{16}\cdot 37^{9}\cdot 107^{2} \)	18T319	Trivial
18.10.334750966203983365623808.1	x^18 - 13x^16 - 10x^15 + 58x^14 + 89x^13 - 98x^12 - 286x^11 - 20x^10 + 429x^9 + 229x^8 - 282x^7 - 227x^6 + 53x^5 + 71x^4 + 5x^3 - 2x^2 + 3x + 1	\( 2^{12}\cdot 13^{2}\cdot 37^{9}\cdot 61^{2} \)	18T319	Trivial (GRH)
18.14.5285331976352154880724992.1	x^18 - 3x^17 - 4x^16 + 9x^15 - 25x^14 + 11x^13 + 105x^12 + 58x^11 - 71x^10 - 273x^9 - 220x^8 + 252x^7 + 374x^6 + 3x^5 - 170x^4 - 64x^3 + 9x^2 + 8x + 1	\( 2^{12}\cdot 23^{2}\cdot 37^{9}\cdot 137^{2} \)	18T319	Trivial (GRH)
18.14.6987344124373460037357568.1	x^18 - 4x^17 - 7x^16 + 30x^15 - 69x^13 + 86x^12 + 46x^11 - 202x^10 - 31x^9 + 157x^8 + 148x^7 - 29x^6 - 187x^5 - 3x^4 + 77x^3 - 4x^2 - 9x + 1	\( 2^{12}\cdot 37^{9}\cdot 3623^{2} \)	18T319	Trivial (GRH)
18.18.142493532772533353405304832.1	x^18 - 3x^17 - 18x^16 + 43x^15 + 143x^14 - 223x^13 - 603x^12 + 508x^11 + 1359x^10 - 505x^9 - 1624x^8 + 146x^7 + 1012x^6 + 93x^5 - 302x^4 - 70x^3 + 31x^2 + 12x + 1	\( 2^{12}\cdot 37^{9}\cdot 16361^{2} \)	18T319	Trivial (GRH)
18.18.512652391182435784215973888.1	x^18 - 25x^16 - 4x^15 + 230x^14 + 55x^13 - 996x^12 - 244x^11 + 2176x^10 + 393x^9 - 2413x^8 - 90x^7 + 1367x^6 - 175x^5 - 347x^4 + 95x^3 + 24x^2 - 11x + 1	\( 2^{12}\cdot 37^{9}\cdot 31033^{2} \)	18T319	Trivial (GRH)