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 23 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.2.335390455497571113631744.1	x^20 + 7x^16 + 6x^12 - 22x^8 - 7x^4 - 1	\( -\,2^{38}\cdot 1051^{4} \)	20T691	Trivial (GRH)
20.2.1157096651100543769378816.1	x^20 - 7x^18 + 23x^16 - 46x^14 + 62x^12 - 57x^10 + 33x^8 - 6x^6 - 6x^4 + 5x^2 - 1	\( -\,2^{20}\cdot 32411^{4} \)	20T691	Trivial (GRH)
20.2.1860495326773308902342656.1	x^20 + 6x^16 + 9x^12 - 4x^8 - 12x^4 - 1	\( -\,2^{20}\cdot 36497^{4} \)	20T691	Trivial (GRH)
20.2.1860495326773308902342656.2	x^20 + 10x^16 + 21x^12 + 4x^8 - 12x^4 - 1	\( -\,2^{20}\cdot 36497^{4} \)	20T691	Trivial (GRH)
20.2.3074707726435761437802496.1	x^20 - x^16 - 2x^8 + 4x^4 - 1	\( -\,2^{20}\cdot 41381^{4} \)	20T691	Trivial (GRH)
20.2.3074707726435761437802496.2	x^20 + 5x^16 + x^12 - 18x^8 - 4x^4 - 1	\( -\,2^{20}\cdot 41381^{4} \)	20T691	Trivial (GRH)
20.6.455293169564857148863676416.1	x^20 - 5x^16 + 9x^12 - 9x^8 + 6x^4 - 1	\( -\,2^{40}\cdot 13^{4}\cdot 347^{4} \)	20T691	Trivial (GRH)
20.6.455293169564857148863676416.2	x^20 - x^16 - 5x^12 + x^8 + 4x^4 - 1	\( -\,2^{40}\cdot 13^{4}\cdot 347^{4} \)	20T691	Trivial (GRH)
20.6.2486366931153398287534391296.1	x^20 - 5x^18 - 19x^16 + 8x^14 + 86x^12 + 131x^10 + 62x^8 - 33x^6 - 49x^4 - 17x^2 - 1	\( -\,2^{20}\cdot 149^{4}\cdot 1481^{4} \)	20T691	Trivial (GRH)
20.6.2486366931153398287534391296.2	x^20 - 5x^18 - x^16 + 26x^14 - x^12 - 40x^10 - 14x^8 + 25x^6 + 16x^4 - 2x^2 - 1	\( -\,2^{20}\cdot 149^{4}\cdot 1481^{4} \)	20T691	Trivial (GRH)
20.12.14569381426075428763637645312.1	x^20 - 8x^18 + 20x^16 - 56x^14 + 356x^12 - 1168x^10 + 1864x^8 - 1600x^6 + 784x^4 - 224x^2 + 32	\( 2^{45}\cdot 13^{4}\cdot 347^{4} \)	20T691	Trivial (GRH)
20.4.20349401981991717600380321792.1	x^20 - 10x^18 + 44x^16 - 112x^14 + 184x^12 - 208x^10 + 168x^8 - 96x^6 + 38x^4 - 12x^2 + 2	\( 2^{57}\cdot 613^{4} \)	20T691	Trivial (GRH)
20.10.1950870747766649155582852857856.1	x^20 - 9x^16 + 27x^12 - 31x^8 + 12x^4 - 1	\( -\,2^{40}\cdot 36497^{4} \)	20T691	Trivial (GRH)
20.10.2433062929616749991460283088896.1	x^20 - 9x^16 + 26x^12 - 29x^8 + 11x^4 - 1	\( -\,2^{40}\cdot 38569^{4} \)	20T691	Trivial (GRH)
20.12.416116102910140320918254787756032.1	x^20 - 14x^18 - 98x^16 + 2168x^14 - 3984x^12 - 76336x^10 + 441792x^8 - 762528x^6 + 332592x^4 - 492128x^2 + 913952	\( 2^{45}\cdot 13^{8}\cdot 347^{4} \)	20T691	Trivial (GRH)
20.12.1741167538834544763439794528727334912.1	x^20 - 31x^18 + 2981x^14 - 2793x^12 - 76738x^10 + 133708x^8 + 563958x^6 - 1495909x^4 + 530453x^2 + 571787	\( 2^{36}\cdot 83^{7}\cdot 983^{4} \)	20T691	Trivial (GRH)
20.20.1741167538834544763439794528727334912.1	x^20 - 61x^18 + 1529x^16 - 20608x^14 + 164027x^12 - 798075x^10 + 2385289x^8 - 4315198x^6 + 4539685x^4 - 2528263x^2 + 571787	\( 2^{36}\cdot 83^{7}\cdot 983^{4} \)	20T691	Trivial (GRH)
20.4.1741167538834544763439794528727334912.1	x^20 + 56x^18 + 1239x^16 + 13660x^14 + 76332x^12 + 170366x^10 - 218299x^8 - 1811192x^6 - 2906660x^4 - 978238x^2 + 571787	\( 2^{36}\cdot 83^{7}\cdot 983^{4} \)	20T691	$[2]$ (GRH)
20.12.1741167538834544763439794528727334912.2	x^20 + 31x^18 - 130x^16 - 4509x^14 + 6325x^12 + 183646x^10 - 154680x^8 - 1713278x^6 + 3802479x^4 - 2610931x^2 + 571787	\( 2^{36}\cdot 83^{7}\cdot 983^{4} \)	20T691	Trivial (GRH)
20.4.74891594867646330033252195969701773312.1	x^20 + 52x^18 + 346x^16 - 41816x^14 - 690725x^12 + 8388608x^10 + 159203891x^8 - 770557196x^6 - 15663050255x^4 - 19231527200x^2 + 117865222327	\( 2^{40}\cdot 4903^{7} \)	20T691	Trivial (GRH)
20.4.74891594867646330033252195969701773312.2	x^20 + 28x^18 + 1454x^16 + 43088x^14 - 8285x^12 + 1953668x^10 + 58287958x^8 - 1144476572x^6 - 5162103938x^4 + 39809261304x^2 + 117865222327	\( 2^{40}\cdot 4903^{7} \)	20T691	Trivial (GRH)
20.20.11994903175031178875336744508402610208768.1	x^20 - 168x^18 + 11277x^16 - 397532x^14 + 8089180x^12 - 98149160x^10 + 709808115x^8 - 2994937638x^6 + 7062713024x^4 - 8447581138x^2 + 3939040643	\( 2^{36}\cdot 83^{9}\cdot 983^{4} \)	20T691	Trivial (GRH)
20.4.11994903175031178875336744508402610208768.1	x^20 + 83x^18 + 1218x^16 - 67415x^14 - 2249383x^12 - 3984498x^10 + 634504456x^8 + 8681848472x^6 + 36806500977x^4 + 40292114529x^2 + 3939040643	\( 2^{36}\cdot 83^{9}\cdot 983^{4} \)	20T691	$[2, 2]$ (GRH)