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 14 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.2.356324486234118630448099.1	x^20 - 3x^19 + 2x^18 + 9x^17 - 21x^16 + 7x^15 + 40x^14 - 44x^13 - 77x^12 + 267x^11 - 331x^10 + 192x^9 + 33x^8 - 176x^7 + 200x^6 - 147x^5 + 86x^4 - 41x^3 + 17x^2 - 4x + 1	\( -\,11^{17}\cdot 89^{3} \)	20T432	Trivial
20.8.3919569348575304934929089.1	x^20 - 3x^19 - 4x^18 + 18x^17 + 9x^16 - 52x^15 - 27x^14 + 97x^13 + 71x^12 - 99x^11 - 131x^10 + 44x^9 + 108x^8 + 17x^7 - 14x^6 - 36x^5 - 18x^4 + 16x^3 + 10x^2 - 7x + 1	\( 11^{18}\cdot 89^{3} \)	20T432	Trivial (GRH)
20.2.33170570354885225234441216.1	x^20 + 4x^18 - 5x^17 + 8x^16 - 16x^15 + 11x^14 - 19x^13 + 15x^12 + 37x^11 - 121x^10 - 65x^9 + 104x^8 + 37x^7 - 103x^6 - 114x^5 - 66x^4 - 38x^3 - 17x^2 - 5x - 1	\( -\,2^{10}\cdot 11^{16}\cdot 89^{3} \)	20T432	Trivial (GRH)
20.6.658618684118710741619590144.1	x^20 - 4x^19 + 9x^18 - 19x^17 + 6x^16 + 11x^15 - 27x^14 + 141x^13 - 118x^12 - 253x^11 + 396x^10 - 163x^9 + 225x^8 - 170x^7 - 31x^6 + 119x^5 - 53x^4 - 11x^3 + 11x^2 - 2x - 1	\( -\,2^{10}\cdot 11^{16}\cdot 241^{3} \)	20T432	Trivial (GRH)
20.0.1544108753590939768502655121.3	x^20 - 8x^19 + 44x^18 - 160x^17 + 455x^16 - 996x^15 + 1810x^14 - 2689x^13 + 3386x^12 - 3482x^11 + 3002x^10 - 2109x^9 + 1325x^8 - 779x^7 + 527x^6 - 347x^5 + 218x^4 - 95x^3 + 33x^2 - 6x + 1	\( 11^{17}\cdot 1451^{3} \)	20T432	Trivial (GRH)
20.0.2005018537548922694563074277.1	x^20 - 4x^19 + x^18 + 14x^17 - 24x^16 - 21x^15 + 164x^14 - 208x^13 - 67x^12 + 551x^11 - 595x^10 - 97x^9 + 985x^8 - 1230x^7 + 860x^6 - 496x^5 + 330x^4 - 187x^3 + 44x^2 + 11x + 11	\( 11^{17}\cdot 1583^{3} \)	20T432	Trivial (GRH)
20.4.14491297883574819995090157568.1	x^20 - 2x^16 - 49x^12 - 119x^8 - 29x^4 + 67	\( 2^{20}\cdot 11^{16}\cdot 67^{3} \)	20T432	Trivial (GRH)
20.4.14491297883574819995090157568.2	x^20 - 8x^18 + 13x^16 + 96x^14 - 460x^12 + 671x^10 + 35x^8 - 1147x^6 + 1267x^4 - 536x^2 + 67	\( 2^{20}\cdot 11^{16}\cdot 67^{3} \)	20T432	Trivial (GRH)
20.10.16985196289500337453529206331.3	x^20 - 8x^19 + 36x^18 - 108x^17 + 230x^16 - 345x^15 + 302x^14 + 28x^13 - 639x^12 + 1314x^11 - 1508x^10 + 591x^9 + 1493x^8 - 2631x^7 + 771x^6 + 1236x^5 - 764x^4 - 72x^3 + 56x^2 + 17x + 1	\( -\,11^{18}\cdot 1451^{3} \)	20T432	Trivial (GRH)
20.8.18079489015266793067734899712.1	x^20 - 19x^16 - 69x^12 + 1701x^8 - 2210x^4 + 727	\( 2^{10}\cdot 11^{16}\cdot 727^{3} \)	20T432	Trivial (GRH)
20.10.22055203913038149640193817047.1	x^20 - 3x^19 - 4x^18 + 18x^17 - 24x^16 - 74x^15 + 138x^14 + 86x^13 - 413x^12 + 275x^11 + 1013x^10 - 638x^9 - 1421x^8 + 182x^7 + 789x^6 + 140x^5 - 128x^4 - 50x^3 - x^2 + 4x + 1	\( -\,11^{18}\cdot 1583^{3} \)	20T432	Trivial (GRH)
20.6.79692860778363999735970407424.1	x^20 - 22x^16 - 165x^12 + 3509x^8 + 2299x^4 - 29161	\( -\,2^{10}\cdot 11^{18}\cdot 241^{3} \)	20T432	Trivial (GRH)
20.20.3172126672449549143567477325812349950492672.1	x^20 - 321x^18 + 39182x^16 - 2362410x^14 + 78516261x^12 - 1521153905x^10 + 17521759023x^8 - 118717836375x^6 + 453844496710x^4 - 896697119210x^2 + 708898288583	\( 2^{20}\cdot 11^{16}\cdot 23^{3}\cdot 419^{6} \)	20T432	Trivial (GRH)
20.20.1678055009725811496947195505354733123810623488.1	x^20 - 554x^18 + 128883x^16 - 16333702x^14 + 1223654732x^12 - 55069019284x^10 + 1451946981565x^8 - 21079412126729x^6 + 150667328531683x^4 - 438902785988869x^2 + 375007194660407	\( 2^{20}\cdot 11^{16}\cdot 23^{5}\cdot 419^{6} \)	20T432	Trivial (GRH)