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 15 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.95777233176300048828125.1	x^20 - 10x^19 + 47x^18 - 134x^17 + 244x^16 - 252x^15 + 14x^14 + 403x^13 - 595x^12 + 136x^11 + 768x^10 - 1227x^9 + 749x^8 + 44x^7 - 325x^6 + 108x^5 + 101x^4 - 108x^3 + 46x^2 - 10x + 1	\( 5^{15}\cdot 11^{12} \)	$C_5\times F_5$ (as 20T29)	Trivial
20.0.2910383045673370361328125.2	x^20 - 2x^15 + 4x^10 - 3x^5 + 1	\( 5^{35} \)	$C_5\times F_5$ (as 20T29)	Trivial (GRH)
20.0.6276856753442000000000000000.1	x^20 - x^19 - 14x^18 + 8x^17 + 84x^16 + 21x^15 - 284x^14 - 856x^13 + 2957x^12 - 2148x^11 - 454x^10 + 442x^9 + 1242x^8 - 2984x^7 + 2070x^6 + 2062x^5 - 2189x^4 - 693x^3 + 572x^2 + 154x + 11	\( 2^{16}\cdot 5^{15}\cdot 11^{12} \)	$C_5\times F_5$ (as 20T29)	$[5]$ (GRH)
20.0.9134028737668995745480060577392578125.1	x^20 - 118x^15 + 4169x^10 - 40172x^5 + 161051	\( 5^{35}\cdot 11^{12} \)	$C_5\times F_5$ (as 20T29)	$[5]$ (GRH)
20.0.9134028737668995745480060577392578125.2	x^20 - 41x^15 + 1881x^10 - 54571x^5 + 1771561	\( 5^{35}\cdot 11^{12} \)	$C_5\times F_5$ (as 20T29)	$[55]$ (GRH)
20.0.254226200642572774598633256129316436767578125.1	x^20 - 8x^19 - 167x^18 + 374x^17 + 17039x^16 + 38288x^15 - 735310x^14 - 5128108x^13 + 7151967x^12 + 188733886x^11 + 569808055x^10 - 2282213678x^9 - 17208973972x^8 - 16433231696x^7 + 214119303238x^6 + 717838125680x^5 - 502397221205x^4 - 7823618530310x^3 - 8270841308686x^2 + 29747851180432x + 86798990281751	\( 5^{15}\cdot 11^{12}\cdot 61^{12} \)	$C_5\times F_5$ (as 20T29)	$[5, 5, 5]$ (GRH)
20.0.93026920175496071256587866935173423923370361328125.1	x^20 - 4x^19 - 180x^18 + 1861x^17 + 41285x^16 + 56486x^15 - 1770231x^14 + 13207675x^13 + 539202114x^12 + 6259348669x^11 + 44724494010x^10 + 229585020498x^9 + 900899023954x^8 + 2784140309493x^7 + 6871932187949x^6 + 13592479679308x^5 + 21415551177601x^4 + 26404835212626x^3 + 24419514025237x^2 + 15370942553698x + 5232878702531	\( 3^{16}\cdot 5^{15}\cdot 11^{12}\cdot 41^{12} \)	$C_5\times F_5$ (as 20T29)	$[5, 5, 5, 1665305]$ (GRH)
20.0.206095568825660384301069002308652852661907672882080078125.1	x^20 - 25947x^15 - 76999681x^10 + 146151013550157x^5 + 3005011477995800801	\( 5^{35}\cdot 11^{12}\cdot 41^{12} \)	$C_5\times F_5$ (as 20T29)	n/a
20.0.1588913754016079841241457850808227729797363281250000000000000000.1	x^20 - 1814102x^15 + 4673959352304x^10 - 43581344807630608x^5 + 331470290341877498625616	\( 2^{16}\cdot 5^{35}\cdot 11^{12}\cdot 61^{12} \)	$C_5\times F_5$ (as 20T29)	n/a
20.0.5736230412297638662801171274018816826654075993118491241455078125.1	x^20 - 2x^19 - 3063x^18 + 56360x^17 + 3725721x^16 - 136176698x^15 - 775112280x^14 + 118143737840x^13 - 2064108884245x^12 - 10834777388248x^11 + 1034359675135247x^10 - 21566981447020668x^9 + 302277263506153992x^8 - 3933531629742272088x^7 + 52433632090043553846x^6 - 622457267869487652912x^5 + 5752830050933993979591x^4 - 38480091547554245555724x^3 + 177378875955066879158870x^2 - 508045130993392801755650x + 725830423259092273389151	\( 5^{15}\cdot 11^{12}\cdot 41^{12}\cdot 61^{12} \)	$C_5\times F_5$ (as 20T29)	n/a
20.0.1365577184056770177137464349146300806980188999019006919566506378173828125.1	x^20 - 4x^19 - 11030x^18 - 349639x^17 + 43133865x^16 + 3165845986x^15 + 3297596774x^14 - 7831652014980x^13 - 366025154454816x^12 - 3519052998417431x^11 + 369783648942913960x^10 + 22397712541078584313x^9 + 716821696556315266424x^8 + 15845552032766343133183x^7 + 260355500215372228216244x^6 + 3260774067552606207924018x^5 + 31182656611119677641118731x^4 + 223683928418871140736442876x^3 + 1152215888689249604582827267x^2 + 3872795249613793564434947278x + 6616039969022180498502070261	\( 5^{15}\cdot 11^{16}\cdot 31^{12}\cdot 181^{12} \)	$C_5\times F_5$ (as 20T29)	n/a
20.0.55151002218183282893941830832304805064658020210266113281250000000000000000.1	x^20 - 2380244x^15 - 16449885784464x^10 - 54627959472340369984x^5 + 526728719890528781692016896	\( 2^{16}\cdot 5^{35}\cdot 11^{12}\cdot 461^{12} \)	$C_5\times F_5$ (as 20T29)	n/a
20.0.2545253286317407470203188318689628626794133961366397273208762363311767578125.1	x^20 - 10x^19 + 50x^18 - 165x^17 + 401x^16 + 29082274x^15 - 257595575x^14 + 1057621205x^13 - 2748329129x^12 + 5145784683x^11 + 771422587822781x^10 - 4170822961364545x^9 + 10946763251886561x^8 - 16613144662595113x^7 + 16782740267443763x^6 + 4211111527467189063284x^5 - 13145794848179964973699x^4 - 3097304809802488626839x^3 + 21237432158942543809016x^2 - 9205451745388989028944x + 6578911714393603275321248551	\( 5^{15}\cdot 11^{12}\cdot 19^{16}\cdot 461^{12} \)	$C_5\times F_5$ (as 20T29)	n/a
20.0.122003826420211264288677099926477115147088065905336526338942348957061767578125.1	x^20 - 78330153x^15 + 2737990582811559x^10 - 24499004414433966486927x^5 + 75302901891158409924316939431	\( 3^{16}\cdot 5^{35}\cdot 31^{12}\cdot 181^{12} \)	$C_5\times F_5$ (as 20T29)	n/a
20.0.1543286938436821377977594364411890979294271079928560077574127388000488281250000000000000000.1	x^20 - 851737518x^15 + 2128761163619493418224x^10 - 2467172500874840049039927482832x^5 + 67777855648151168856132999894099006781776	\( 2^{16}\cdot 3^{16}\cdot 5^{35}\cdot 11^{12}\cdot 41^{12}\cdot 61^{12} \)	$C_5\times F_5$ (as 20T29)	n/a