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 matches 1-50 of 60)

Label	Polynomial	Discriminant	Galois group	Class group
20.8.16793894275362398486328125.1	x^20 - 2x^19 - 10x^18 + 14x^17 + 43x^16 - 32x^15 - 102x^14 + 37x^13 + 167x^12 - 18x^11 - 195x^10 - 18x^9 + 167x^8 + 37x^7 - 102x^6 - 32x^5 + 43x^4 + 14x^3 - 10x^2 - 2x + 1	\( 5^{11}\cdot 61^{4}\cdot 397^{4} \)	20T802	Trivial (GRH)
20.0.46079291032371200000000000.1	x^20 + 10x^18 + 46x^16 + 127x^14 + 230x^12 + 286x^10 + 254x^8 + 166x^6 + 79x^4 + 25x^2 + 5	\( 2^{24}\cdot 5^{11}\cdot 487^{4} \)	20T802	Trivial (GRH)
20.4.46079291032371200000000000.1	x^20 - 10x^18 + 46x^16 - 127x^14 + 230x^12 - 286x^10 + 254x^8 - 166x^6 + 79x^4 - 25x^2 + 5	\( 2^{24}\cdot 5^{11}\cdot 487^{4} \)	20T802	Trivial (GRH)
20.0.52231705632000000000000000.1	x^20 - x^16 + 5x^14 + 4x^12 + 10x^8 + 15x^6 + 5x^4 + 5x^2 + 5	\( 2^{20}\cdot 3^{4}\cdot 5^{15}\cdot 67^{4} \)	20T802	Trivial (GRH)
20.4.52231705632000000000000000.1	x^20 + 3x^18 - 5x^16 - 34x^14 - 51x^12 - 20x^10 - 40x^6 - 55x^4 - 15x^2 + 5	\( 2^{20}\cdot 3^{4}\cdot 5^{15}\cdot 67^{4} \)	20T802	Trivial (GRH)
20.8.22959484172585057647705078125.1	x^20 - 2x^19 - 5x^18 - 14x^17 + 13x^16 + 36x^15 + 39x^14 + 392x^13 - 77x^12 - 71x^11 + 201x^10 - 665x^9 - 17x^8 + 105x^7 - 90x^6 + 279x^5 - 132x^4 - 2x^3 + 16x^2 - 7x + 1	\( 3^{4}\cdot 5^{15}\cdot 23^{6}\cdot 89^{4} \)	20T802	Trivial (GRH)
20.0.41316635395822879565166861037.1	x^20 - 6x^19 + 21x^18 - 65x^17 + 183x^16 - 447x^15 + 1041x^14 - 2083x^13 + 3720x^12 - 7065x^11 + 13310x^10 - 20559x^9 + 28783x^8 - 41818x^7 + 51167x^6 - 50733x^5 + 46826x^4 - 33325x^3 + 18469x^2 - 7672x + 1889	\( 13^{13}\cdot 97^{2}\cdot 347^{4} \)	20T802	$[2]$ (GRH)
20.12.62490080598623484767626953125.1	x^20 - 3x^19 - 9x^18 + 7x^17 + 48x^16 + 113x^15 + 34x^14 - 550x^13 - 1087x^12 - 69x^11 + 1942x^10 + 2279x^9 + 364x^8 - 1797x^7 - 2097x^6 - 674x^5 + 459x^4 + 585x^3 + 265x^2 + 25x - 5	\( 5^{11}\cdot 61^{6}\cdot 397^{4} \)	20T802	Trivial (GRH)
20.8.62490080598623484767626953125.1	x^20 - 8x^19 + 17x^18 + 35x^17 - 227x^16 + 355x^15 + 108x^14 - 1192x^13 + 2192x^12 - 2816x^11 + 2328x^10 + 821x^9 - 3449x^8 - 470x^7 + 7813x^6 - 9924x^5 + 6536x^4 - 3268x^3 + 1791x^2 - 773x + 131	\( 5^{11}\cdot 61^{6}\cdot 397^{4} \)	20T802	Trivial (GRH)
20.8.91395200000000000000000000000.1	x^20 + 5x^18 - 15x^16 - 70x^14 - 5x^12 + 180x^10 + 80x^8 - 400x^6 + 290x^4 - 75x^2 + 5	\( 2^{28}\cdot 5^{23}\cdot 13^{4} \)	20T802	Trivial (GRH)
20.0.91395200000000000000000000000.2	x^20 + 15x^18 + 90x^16 + 275x^14 + 450x^12 + 390x^10 + 240x^8 + 295x^6 + 315x^4 + 125x^2 + 5	\( 2^{28}\cdot 5^{23}\cdot 13^{4} \)	20T802	$[2, 2]$ (GRH)
20.12.91395200000000000000000000000.2	x^20 - 15x^18 + 90x^16 - 275x^14 + 450x^12 - 390x^10 + 240x^8 - 295x^6 + 315x^4 - 125x^2 + 5	\( 2^{28}\cdot 5^{23}\cdot 13^{4} \)	20T802	Trivial (GRH)
20.4.91395200000000000000000000000.2	x^20 - 5x^18 - 15x^16 + 70x^14 - 5x^12 - 180x^10 + 80x^8 + 400x^6 + 290x^4 + 75x^2 + 5	\( 2^{28}\cdot 5^{23}\cdot 13^{4} \)	20T802	$[2]$ (GRH)
20.8.91395200000000000000000000000.2	x^20 - 10x^18 + 40x^16 - 80x^14 + 35x^12 + 145x^10 - 405x^8 + 350x^6 - 60x^4 - 25x^2 + 5	\( 2^{28}\cdot 5^{23}\cdot 13^{4} \)	20T802	Trivial (GRH)
20.4.91395200000000000000000000000.3	x^20 + 10x^18 + 40x^16 + 80x^14 + 35x^12 - 145x^10 - 405x^8 - 350x^6 - 60x^4 + 25x^2 + 5	\( 2^{28}\cdot 5^{23}\cdot 13^{4} \)	20T802	Trivial (GRH)
20.8.91395200000000000000000000000.3	x^20 - 5x^18 + 20x^16 + 55x^14 - 150x^12 - 375x^10 - 15x^8 + 255x^6 + 15x^4 - 50x^2 + 5	\( 2^{28}\cdot 5^{23}\cdot 13^{4} \)	20T802	Trivial (GRH)
20.4.91395200000000000000000000000.4	x^20 + 5x^18 + 20x^16 - 55x^14 - 150x^12 + 375x^10 - 15x^8 - 255x^6 + 15x^4 + 50x^2 + 5	\( 2^{28}\cdot 5^{23}\cdot 13^{4} \)	20T802	Trivial (GRH)
20.8.91395200000000000000000000000.4	x^20 - 10x^18 + 40x^16 - 75x^14 + 40x^12 + 90x^10 - 170x^8 + 90x^6 + 15x^4 - 25x^2 + 5	\( 2^{28}\cdot 5^{23}\cdot 13^{4} \)	20T802	Trivial (GRH)
20.4.91395200000000000000000000000.5	x^20 + 10x^18 + 40x^16 + 75x^14 + 40x^12 - 90x^10 - 170x^8 - 90x^6 + 15x^4 + 25x^2 + 5	\( 2^{28}\cdot 5^{23}\cdot 13^{4} \)	20T802	Trivial (GRH)
20.12.158013751236884807357861328125.1	x^20 - x^19 - 12x^18 + 13x^17 + 35x^16 - 48x^15 + 2x^14 + 36x^13 + 247x^12 - 302x^11 - 1711x^10 + 2899x^9 + 366x^8 - 4888x^7 + 6101x^6 - 3067x^5 - 159x^4 + 739x^3 - 249x^2 + 28x - 1	\( 5^{11}\cdot 61^{4}\cdot 97^{2}\cdot 397^{4} \)	20T802	Trivial (GRH)
20.12.206635357553265518829345703125.1	x^20 - 5x^19 + 40x^17 - 95x^16 + 84x^15 + 125x^14 - 705x^13 + 1475x^12 - 925x^11 - 2884x^10 + 7465x^9 - 5215x^8 - 5810x^7 + 14195x^6 - 8921x^5 - 3390x^4 + 8715x^3 - 5595x^2 + 1625x - 179	\( 3^{6}\cdot 5^{15}\cdot 23^{6}\cdot 89^{4} \)	20T802	Trivial (GRH)
20.4.267741240538215680000000000000.1	x^20 + 8x^18 + 29x^16 + 97x^14 + 296x^12 + 350x^10 - 1255x^8 - 3750x^6 - 2925x^4 - 375x^2 + 125	\( 2^{20}\cdot 5^{13}\cdot 3803^{4} \)	20T802	Trivial (GRH)
20.8.267741240538215680000000000000.1	x^20 - 11x^18 + 16x^16 + 114x^14 - 214x^12 - 395x^10 + 830x^8 + 750x^6 - 525x^4 - 250x^2 + 125	\( 2^{20}\cdot 5^{13}\cdot 3803^{4} \)	20T802	Trivial (GRH)
20.12.267741240538215680000000000000.2	x^20 - 6x^18 + 16x^16 - 171x^14 + 1011x^12 - 2415x^10 + 2855x^8 - 2175x^6 + 1375x^4 - 625x^2 + 125	\( 2^{20}\cdot 5^{13}\cdot 3803^{4} \)	20T802	Trivial (GRH)
20.4.267741240538215680000000000000.2	x^20 + 9x^18 + 40x^16 + 97x^14 + 69x^12 - 115x^10 - 795x^8 - 2250x^6 - 2225x^4 - 375x^2 + 125	\( 2^{20}\cdot 5^{13}\cdot 3803^{4} \)	20T802	Trivial (GRH)
20.8.267741240538215680000000000000.2	x^20 - 14x^18 + 75x^16 - 157x^14 - 161x^12 + 1615x^10 - 3685x^8 + 3850x^6 - 1525x^4 - 125x^2 + 125	\( 2^{20}\cdot 5^{13}\cdot 3803^{4} \)	20T802	Trivial (GRH)
20.12.573987104314626441192626953125.1	x^20 - 10x^19 + 50x^18 - 165x^17 + 340x^16 - 272x^15 - 670x^14 + 2820x^13 - 4875x^12 + 3640x^11 + 1949x^10 - 7210x^9 + 6575x^8 - 1000x^7 - 3155x^6 + 2727x^5 - 595x^4 - 330x^3 + 180x^2 - 9	\( 3^{4}\cdot 5^{17}\cdot 23^{6}\cdot 89^{4} \)	20T802	Trivial (GRH)
20.16.5165883938831637970733642578125.2	x^20 - 2x^19 - 18x^18 + 41x^17 + 81x^16 - 270x^15 + 221x^14 + 269x^13 - 2333x^12 + 4187x^11 + 3172x^10 - 18357x^9 + 10737x^8 + 28511x^7 - 34369x^6 - 14280x^5 + 33336x^4 - 4181x^3 - 10753x^2 + 4077x - 79	\( 3^{6}\cdot 5^{17}\cdot 23^{6}\cdot 89^{4} \)	20T802	Trivial (GRH)
20.12.12145567127297495495635986328125.1	x^20 - 2x^19 - 17x^18 + 15x^17 + 88x^16 + 83x^15 - 522x^14 - 1212x^13 + 1417x^12 + 3182x^11 + 2754x^10 - 2198x^9 - 11863x^8 - 121x^7 + 2620x^6 - 2777x^5 + 11792x^4 + 5447x^3 - 3558x^2 - 69x + 41	\( 3^{4}\cdot 5^{15}\cdot 23^{8}\cdot 89^{4} \)	20T802	Trivial (GRH)
20.16.12145567127297495495635986328125.1	x^20 - 10x^19 + 13x^18 + 160x^17 - 476x^16 - 827x^15 + 4112x^14 + 828x^13 - 16124x^12 + 5527x^11 + 32434x^10 - 16632x^9 - 37564x^8 + 17434x^7 + 30545x^6 - 14678x^5 - 9757x^4 + 4409x^3 + 874x^2 - 311x + 41	\( 3^{4}\cdot 5^{15}\cdot 23^{8}\cdot 89^{4} \)	20T802	Trivial (GRH)
20.12.42279623745384992000000000000000.1	x^20 + 4x^18 - 28x^16 - 64x^14 + 241x^12 - 60x^10 - 260x^8 + 170x^6 + 25x^4 - 35x^2 + 5	\( 2^{20}\cdot 5^{15}\cdot 6029^{4} \)	20T802	Trivial (GRH)
20.16.42279623745384992000000000000000.1	x^20 - 18x^18 + 95x^16 - 161x^14 - 116x^12 + 620x^10 - 495x^8 - 135x^6 + 280x^4 - 75x^2 + 5	\( 2^{20}\cdot 5^{15}\cdot 6029^{4} \)	20T802	Trivial (GRH)
20.8.42279623745384992000000000000000.1	x^20 + 11x^18 + 30x^16 - 37x^14 - 226x^12 - 65x^10 + 460x^8 + 255x^6 - 225x^4 - 120x^2 + 5	\( 2^{20}\cdot 5^{15}\cdot 6029^{4} \)	20T802	Trivial (GRH)
20.12.42279623745384992000000000000000.2	x^20 - 2x^18 - 22x^16 + 48x^14 + 106x^12 - 310x^10 + 80x^8 + 225x^6 - 85x^4 - 45x^2 + 5	\( 2^{20}\cdot 5^{15}\cdot 6029^{4} \)	20T802	Trivial (GRH)
20.16.42279623745384992000000000000000.2	x^20 - 19x^18 + 97x^16 - 46x^14 - 649x^12 + 1045x^10 + 565x^8 - 2225x^6 + 1595x^4 - 370x^2 + 5	\( 2^{20}\cdot 5^{15}\cdot 6029^{4} \)	20T802	Trivial (GRH)
20.4.42279623745384992000000000000000.2	x^20 + 13x^18 + 54x^16 + 32x^14 - 349x^12 - 960x^10 - 820x^8 + 165x^6 + 605x^4 + 245x^2 + 5	\( 2^{20}\cdot 5^{15}\cdot 6029^{4} \)	20T802	$[3]$ (GRH)
20.8.42279623745384992000000000000000.2	x^20 + 6x^18 - 39x^16 - 189x^14 + 181x^12 + 1120x^10 + 890x^8 - 50x^6 - 150x^4 + 5	\( 2^{20}\cdot 5^{15}\cdot 6029^{4} \)	20T802	Trivial (GRH)
20.12.42279623745384992000000000000000.3	x^20 - 16x^18 + 35x^16 + 297x^14 - 951x^12 + 575x^10 + 325x^8 - 245x^6 - 50x^4 + 25x^2 + 5	\( 2^{20}\cdot 5^{15}\cdot 6029^{4} \)	20T802	Trivial (GRH)
20.4.42279623745384992000000000000000.3	x^20 + 4x^18 - 54x^16 - 166x^14 + 481x^12 + 2215x^10 + 2930x^8 + 1830x^6 + 585x^4 + 90x^2 + 5	\( 2^{20}\cdot 5^{15}\cdot 6029^{4} \)	20T802	Trivial (GRH)
20.8.42279623745384992000000000000000.3	x^20 - 3x^18 - 17x^16 + 27x^14 + 106x^12 - 10x^10 - 190x^8 - 130x^6 + 5x^4 + 25x^2 + 5	\( 2^{20}\cdot 5^{15}\cdot 6029^{4} \)	20T802	Trivial (GRH)
20.12.42279623745384992000000000000000.4	x^20 - 16x^18 + 80x^16 - 78x^14 - 341x^12 + 495x^10 + 300x^8 - 600x^6 + 70x^4 + 85x^2 + 5	\( 2^{20}\cdot 5^{15}\cdot 6029^{4} \)	20T802	Trivial (GRH)
20.4.42279623745384992000000000000000.4	x^20 + 14x^18 + 55x^16 + 2x^14 - 426x^12 - 940x^10 - 640x^8 + 215x^6 + 450x^4 + 155x^2 + 5	\( 2^{20}\cdot 5^{15}\cdot 6029^{4} \)	20T802	$[3]$ (GRH)
20.8.42279623745384992000000000000000.4	x^20 - 5x^18 - 81x^16 - 90x^14 + 659x^12 + 1535x^10 + 905x^8 - 35x^6 - 135x^4 - 10x^2 + 5	\( 2^{20}\cdot 5^{15}\cdot 6029^{4} \)	20T802	Trivial (GRH)
20.12.42279623745384992000000000000000.5	x^20 - x^18 - 54x^16 + 24x^14 + 781x^12 - 265x^10 - 3135x^8 + 1205x^6 + 35x^4 - 55x^2 + 5	\( 2^{20}\cdot 5^{15}\cdot 6029^{4} \)	20T802	Trivial (GRH)
20.4.42279623745384992000000000000000.5	x^20 + 8x^18 - 119x^14 - 206x^12 + 245x^10 + 850x^8 + 775x^6 + 325x^4 + 65x^2 + 5	\( 2^{20}\cdot 5^{15}\cdot 6029^{4} \)	20T802	Trivial (GRH)
20.8.42279623745384992000000000000000.5	x^20 + 5x^18 - 34x^16 - 60x^14 + 229x^12 + 155x^10 - 445x^8 - 65x^6 + 155x^4 + 55x^2 + 5	\( 2^{20}\cdot 5^{15}\cdot 6029^{4} \)	20T802	Trivial (GRH)
20.8.42279623745384992000000000000000.6	x^20 - 4x^18 - 55x^16 - 42x^14 + 479x^12 + 920x^10 - 530x^8 - 2250x^6 - 1350x^4 - 145x^2 + 5	\( 2^{20}\cdot 5^{15}\cdot 6029^{4} \)	20T802	Trivial (GRH)
20.8.42279623745384992000000000000000.7	x^20 - 9x^18 + 5x^16 + 93x^14 - 16x^12 - 330x^10 - 300x^8 - 5x^6 + 95x^4 + 40x^2 + 5	\( 2^{20}\cdot 5^{15}\cdot 6029^{4} \)	20T802	Trivial (GRH)
20.16.1465621300755332525247833251953125.1	x^20 - 3x^19 - 38x^18 + 148x^17 + 394x^16 - 2324x^15 - 219x^14 + 15540x^13 - 18624x^12 - 39697x^11 + 113953x^10 - 28380x^9 - 262419x^8 + 332408x^7 + 208344x^6 - 598148x^5 + 55887x^4 + 432233x^3 - 143919x^2 - 112287x + 47569	\( 5^{15}\cdot 6029^{6} \)	20T802	Trivial (GRH)
20.16.1465621300755332525247833251953125.2	x^20 - 2x^19 - 29x^18 + 41x^17 + 340x^16 - 193x^15 - 2475x^14 + 4x^13 + 10981x^12 + 1491x^11 - 22264x^10 - 15666x^9 + 25697x^8 + 46644x^7 - 33259x^6 - 41330x^5 + 29993x^4 + 3317x^3 - 3160x^2 - 91x + 49	\( 5^{15}\cdot 6029^{6} \)	20T802	Trivial (GRH)