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
20.8.8694519846067650027294539381.1	x^20 - 7x^18 - 4x^17 + 3x^16 + 18x^15 + 20x^14 - 85x^13 - 11x^12 + 290x^11 + 214x^10 + 78x^9 + 60x^8 - 127x^7 - 95x^6 - 49x^5 - 47x^4 - 3x^3 + 4x^2 + 2x + 1	\( 11^{16}\cdot 5741^{3} \)	20T335	Trivial (GRH)
20.20.218454818255016653811965258323969.1	x^20 - x^19 - 32x^18 + 8x^17 + 411x^16 + 150x^15 - 2653x^14 - 2356x^13 + 8718x^12 + 12524x^11 - 11678x^10 - 29655x^9 - 4375x^8 + 26600x^7 + 20826x^6 + 189x^5 - 5804x^4 - 2028x^3 + 208x^2 + 224x + 32	\( 11^{16}\cdot 109^{2}\cdot 7369^{3} \)	20T335	Trivial (GRH)
20.0.9116864842110232195020398925971456.1	x^20 + 29x^18 + 361x^16 + 2539x^14 + 11180x^12 + 32258x^10 + 61918x^8 + 78302x^6 + 62633x^4 + 28705x^2 + 5741	\( 2^{20}\cdot 11^{16}\cdot 5741^{3} \)	20T335	$[1762]$ (GRH)
20.12.9116864842110232195020398925971456.1	x^20 - 13x^18 + 5x^16 + 415x^14 - 723x^12 - 4065x^10 + 7365x^8 + 12275x^6 - 15151x^4 - 5741x^2 + 5741	\( 2^{20}\cdot 11^{16}\cdot 5741^{3} \)	20T335	Trivial (GRH)
20.20.9116864842110232195020398925971456.1	x^20 - 29x^18 + 361x^16 - 2539x^14 + 11180x^12 - 32258x^10 + 61918x^8 - 78302x^6 + 62633x^4 - 28705x^2 + 5741	\( 2^{20}\cdot 11^{16}\cdot 5741^{3} \)	20T335	Trivial (GRH)
20.0.19280067292868642604792128836993024.1	x^20 + 32x^18 + 424x^16 + 3097x^14 + 13945x^12 + 40764x^10 + 78842x^8 + 100146x^6 + 80304x^4 + 36845x^2 + 7369	\( 2^{20}\cdot 11^{16}\cdot 7369^{3} \)	20T335	$[2, 1090]$ (GRH)
20.12.19280067292868642604792128836993024.1	x^20 + 4x^18 - 69x^16 - 131x^14 + 1718x^12 + 233x^10 - 15094x^8 + 13509x^6 + 25127x^4 - 29476x^2 + 7369	\( 2^{20}\cdot 11^{16}\cdot 7369^{3} \)	20T335	Trivial (GRH)
20.8.19280067292868642604792128836993024.1	x^20 - 4x^18 - 69x^16 + 131x^14 + 1718x^12 - 233x^10 - 15094x^8 - 13509x^6 + 25127x^4 + 29476x^2 + 7369	\( 2^{20}\cdot 11^{16}\cdot 7369^{3} \)	20T335	$[2]$ (GRH)
20.16.707186427206104304235011435350982656.1	x^20 - 24x^18 + 203x^16 - 564x^14 - 1317x^12 + 10070x^10 - 13359x^8 - 7272x^6 + 10292x^4 - 2892x^2 + 241	\( 2^{40}\cdot 11^{16}\cdot 241^{3} \)	20T335	Trivial (GRH)
20.4.707186427206104304235011435350982656.1	x^20 + 24x^18 + 203x^16 + 564x^14 - 1317x^12 - 10070x^10 - 13359x^8 + 7272x^6 + 10292x^4 + 2892x^2 + 241	\( 2^{40}\cdot 11^{16}\cdot 241^{3} \)	20T335	$[2, 2]$ (GRH)
20.4.92832438244258564416940225807466334869.1	x^20 - 3x^19 - 27x^18 + 106x^17 - 601x^16 + 3341x^15 - 6012x^14 + 6576x^13 - 5535x^12 - 105035x^11 + 390034x^10 - 280392x^9 - 517848x^8 + 2687586x^7 - 10762044x^6 + 17754166x^5 + 10928294x^4 - 81796339x^3 + 122959250x^2 - 84055216x + 22936847	\( 11^{16}\cdot 23^{2}\cdot 1563101^{3} \)	20T335	Trivial (GRH)
20.16.41074094878557744094273699176620423643136.1	x^20 - 60x^18 + 804x^16 + 9728x^14 - 242923x^12 + 1170494x^10 + 1345164x^8 - 21552148x^6 + 50119324x^4 - 44954694x^2 + 13997521	\( 2^{40}\cdot 11^{16}\cdot 241^{5} \)	20T335	Trivial (GRH)