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 44 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.83185135558707200000000000.1	x^20 - 4x^18 + 3x^16 + 14x^14 - 17x^12 - 12x^10 + 32x^8 + 18x^6 - 4x^4 + 5x^2 + 5	\( 2^{20}\cdot 5^{11}\cdot 1129^{4} \)	20T755	Trivial (GRH)
20.4.83185135558707200000000000.1	x^20 + 4x^18 + 3x^16 - 14x^14 - 17x^12 + 12x^10 + 32x^8 - 18x^6 - 4x^4 - 5x^2 + 5	\( 2^{20}\cdot 5^{11}\cdot 1129^{4} \)	20T755	Trivial (GRH)
20.0.83185135558707200000000000.2	x^20 + 5x^18 + 19x^16 + 48x^14 + 93x^12 + 136x^10 + 154x^8 + 131x^6 + 79x^4 + 30x^2 + 5	\( 2^{20}\cdot 5^{11}\cdot 1129^{4} \)	20T755	Trivial (GRH)
20.4.83185135558707200000000000.2	x^20 - 3x^18 + 4x^16 - 6x^14 + 8x^12 + 5x^10 - 27x^8 + 18x^6 + 14x^4 - 20x^2 + 5	\( 2^{20}\cdot 5^{11}\cdot 1129^{4} \)	20T755	Trivial (GRH)
20.8.463411895518467200000000000.1	x^20 - 3x^19 - 5x^18 + 17x^17 - 12x^16 - 9x^15 + 43x^14 - 39x^13 + 4x^12 + 33x^11 - 59x^10 + 33x^9 + 4x^8 - 39x^7 + 43x^6 - 9x^5 - 12x^4 + 17x^3 - 5x^2 - 3x + 1	\( 2^{16}\cdot 5^{11}\cdot 3469^{4} \)	20T755	Trivial (GRH)
20.12.7414590328295475200000000000.1	x^20 - 4x^19 - 9x^18 + 42x^17 + 33x^16 - 154x^15 - 124x^14 + 270x^13 + 393x^12 - 178x^11 - 771x^10 - 80x^9 + 659x^8 + 456x^7 - 252x^6 - 546x^5 + 99x^4 + 226x^3 - 41x^2 - 20x - 1	\( 2^{20}\cdot 5^{11}\cdot 3469^{4} \)	20T755	Trivial (GRH)
20.8.7414590328295475200000000000.1	x^20 - 4x^19 - 6x^18 + 12x^17 + x^16 + 8x^15 - 8x^13 + 14x^12 - 24x^11 + 28x^10 - 24x^9 + 14x^8 - 8x^7 + 8x^5 + x^4 + 12x^3 - 6x^2 - 4x + 1	\( 2^{20}\cdot 5^{11}\cdot 3469^{4} \)	20T755	Trivial (GRH)
20.12.7414590328295475200000000000.2	x^20 - 2x^19 - 14x^18 + 24x^17 + 80x^16 - 64x^15 - 360x^14 - 108x^13 + 1438x^12 + 598x^11 - 3548x^10 - 852x^9 + 4992x^8 + 580x^7 - 3988x^6 - 220x^5 + 1644x^4 + 160x^3 - 360x^2 - 20x + 20	\( 2^{20}\cdot 5^{11}\cdot 3469^{4} \)	20T755	Trivial (GRH)
20.4.34843561790753768585205078125.1	x^20 - 4x^19 - 2x^18 + 27x^17 - 28x^16 - 71x^15 + 109x^14 + 238x^13 - 715x^12 + 559x^11 + 465x^10 - 1132x^9 - 346x^8 + 5123x^7 - 13689x^6 + 22909x^5 - 28282x^4 + 27828x^3 - 20808x^2 + 10968x - 3089	\( 5^{15}\cdot 97^{2}\cdot 3319^{4} \)	20T755	Trivial (GRH)
20.16.118633445252727603200000000000.1	x^20 - 6x^19 - 2x^18 + 68x^17 - 53x^16 - 288x^15 + 114x^14 + 1288x^13 - 356x^12 - 4480x^11 + 4204x^10 + 3960x^9 - 6770x^8 + 584x^7 + 3098x^6 - 980x^5 - 577x^4 + 170x^3 + 50x^2 - 4x - 1	\( 2^{24}\cdot 5^{11}\cdot 3469^{4} \)	20T755	Trivial (GRH)
20.4.118633445252727603200000000000.1	x^20 + 10x^18 - 19x^16 - 344x^14 - 382x^12 + 648x^10 + 1446x^8 + 1072x^6 + 389x^4 + 70x^2 + 5	\( 2^{24}\cdot 5^{11}\cdot 3469^{4} \)	20T755	Trivial (GRH)
20.8.118633445252727603200000000000.1	x^20 - 11x^18 + 23x^16 + 86x^14 - 207x^12 - 393x^10 + 397x^8 + 1002x^6 + 571x^4 + 105x^2 + 5	\( 2^{24}\cdot 5^{11}\cdot 3469^{4} \)	20T755	Trivial (GRH)
20.16.118633445252727603200000000000.2	x^20 - 2x^19 - 17x^18 + 28x^17 + 93x^16 - 174x^15 - 178x^14 + 568x^13 - 81x^12 - 854x^11 + 945x^10 + 192x^9 - 2093x^8 + 642x^7 + 2336x^6 - 332x^5 - 1113x^4 - 4x^3 + 185x^2 + 14x - 1	\( 2^{24}\cdot 5^{11}\cdot 3469^{4} \)	20T755	Trivial (GRH)
20.4.118633445252727603200000000000.2	x^20 + 14x^18 + 41x^16 - 128x^14 - 622x^12 - 300x^10 + 1282x^8 + 1744x^6 + 749x^4 + 110x^2 + 5	\( 2^{24}\cdot 5^{11}\cdot 3469^{4} \)	20T755	Trivial (GRH)
20.8.118633445252727603200000000000.2	x^20 - 2x^19 - 11x^18 + 32x^17 + 25x^16 - 180x^15 + 150x^14 + 366x^13 - 979x^12 + 336x^11 + 1845x^10 - 2914x^9 + 401x^8 + 4316x^7 - 5680x^6 + 592x^5 + 4385x^4 - 5366x^3 + 1757x^2 + 864x + 31	\( 2^{24}\cdot 5^{11}\cdot 3469^{4} \)	20T755	Trivial (GRH)
20.12.1898135124043641651200000000000.1	x^20 - 17x^18 + 51x^16 + 138x^14 - 371x^12 - 307x^10 + 761x^8 + 118x^6 - 489x^4 + 135x^2 + 5	\( 2^{28}\cdot 5^{11}\cdot 3469^{4} \)	20T755	Trivial (GRH)
20.16.1898135124043641651200000000000.1	x^20 - 10x^18 - 19x^16 + 344x^14 - 382x^12 - 648x^10 + 1446x^8 - 1072x^6 + 389x^4 - 70x^2 + 5	\( 2^{28}\cdot 5^{11}\cdot 3469^{4} \)	20T755	Trivial (GRH)
20.4.1898135124043641651200000000000.1	x^20 + 24x^18 + 236x^16 + 1232x^14 + 3668x^12 + 6120x^10 + 4912x^8 + 464x^6 - 1616x^4 - 560x^2 + 80	\( 2^{28}\cdot 5^{11}\cdot 3469^{4} \)	20T755	Trivial (GRH)
20.8.1898135124043641651200000000000.1	x^20 + 14x^18 + x^16 - 328x^14 - 302x^12 + 2340x^10 + 1882x^8 - 4776x^6 - 51x^4 + 190x^2 + 5	\( 2^{28}\cdot 5^{11}\cdot 3469^{4} \)	20T755	Trivial (GRH)
20.12.1898135124043641651200000000000.2	x^20 + 11x^18 + 23x^16 - 86x^14 - 207x^12 + 393x^10 + 397x^8 - 1002x^6 + 571x^4 - 105x^2 + 5	\( 2^{28}\cdot 5^{11}\cdot 3469^{4} \)	20T755	Trivial (GRH)
20.16.1898135124043641651200000000000.2	x^20 - 14x^18 + 41x^16 + 128x^14 - 622x^12 + 300x^10 + 1282x^8 - 1744x^6 + 749x^4 - 110x^2 + 5	\( 2^{28}\cdot 5^{11}\cdot 3469^{4} \)	20T755	Trivial (GRH)
20.4.1898135124043641651200000000000.2	x^20 + 27x^18 + 259x^16 + 1114x^14 + 1993x^12 + 125x^10 - 3447x^8 - 2662x^6 - 641x^4 - 25x^2 + 5	\( 2^{28}\cdot 5^{11}\cdot 3469^{4} \)	20T755	Trivial (GRH)
20.8.1898135124043641651200000000000.2	x^20 - 8x^19 + 24x^18 - 56x^17 + 208x^16 - 586x^15 + 990x^14 - 1728x^13 + 3568x^12 - 4900x^11 + 5086x^10 - 7044x^9 + 7604x^8 - 4556x^7 + 3980x^6 - 3356x^5 + 536x^4 - 80x^3 + 184x^2 + 88x + 4	\( 2^{28}\cdot 5^{11}\cdot 3469^{4} \)	20T755	Trivial (GRH)
20.12.1898135124043641651200000000000.3	x^20 - 13x^18 - x^16 + 302x^14 - 187x^12 - 791x^10 + 361x^8 + 566x^6 - 69x^4 - 85x^2 + 5	\( 2^{28}\cdot 5^{11}\cdot 3469^{4} \)	20T755	Trivial (GRH)
20.12.1898135124043641651200000000000.4	x^20 - 21x^18 + 151x^16 - 394x^14 - 47x^12 + 1553x^10 - 971x^8 - 1762x^6 + 771x^4 + 475x^2 + 5	\( 2^{28}\cdot 5^{11}\cdot 3469^{4} \)	20T755	Trivial (GRH)
20.8.2965836131318190080000000000000.1	x^20 + 9x^18 - 33x^16 - 334x^14 + 281x^12 + 3435x^10 + 225x^8 - 7950x^6 - 2925x^4 + 625x^2 + 125	\( 2^{24}\cdot 5^{13}\cdot 3469^{4} \)	20T755	Trivial (GRH)
20.8.2965836131318190080000000000000.2	x^20 - 6x^19 + 11x^18 - 18x^17 + 67x^16 - 124x^15 + 76x^14 - 164x^13 - 43x^12 + 1012x^11 - 1203x^10 - 232x^9 - 463x^8 + 6362x^7 - 9302x^6 + 3616x^5 + 3473x^4 - 3358x^3 - 35x^2 + 454x + 31	\( 2^{24}\cdot 5^{13}\cdot 3469^{4} \)	20T755	Trivial (GRH)
20.0.3883103693091872000000000000000.1	x^20 + 15x^18 + 35x^16 - 100x^14 + 300x^12 + 3750x^10 + 9875x^8 + 18750x^6 + 29375x^4 + 21875x^2 + 3125	\( 2^{20}\cdot 5^{15}\cdot 3319^{4} \)	20T755	$[2]$ (GRH)
20.4.3883103693091872000000000000000.1	x^20 + 20x^18 + 150x^16 + 575x^14 + 1325x^12 + 1125x^10 - 3625x^8 - 12500x^6 - 25000x^4 - 15625x^2 + 3125	\( 2^{20}\cdot 5^{15}\cdot 3319^{4} \)	20T755	Trivial (GRH)
20.8.3883103693091872000000000000000.1	x^20 + 5x^18 - 5x^16 - 200x^14 - 1100x^12 + 1875x^10 + 1000x^8 + 8750x^6 - 11250x^4 - 6250x^2 + 3125	\( 2^{20}\cdot 5^{15}\cdot 3319^{4} \)	20T755	Trivial (GRH)
20.0.3883103693091872000000000000000.2	x^20 + 20x^18 + 140x^16 + 400x^14 + 350x^12 + 3250x^8 + 15625x^6 + 25625x^4 + 15625x^2 + 3125	\( 2^{20}\cdot 5^{15}\cdot 3319^{4} \)	20T755	$[2]$ (GRH)
20.12.3883103693091872000000000000000.2	x^20 - 20x^18 + 120x^16 - 50x^14 - 1650x^12 + 3875x^10 + 3250x^8 - 20625x^6 + 29375x^4 - 18750x^2 + 3125	\( 2^{20}\cdot 5^{15}\cdot 3319^{4} \)	20T755	Trivial (GRH)
20.4.3883103693091872000000000000000.2	x^20 + 15x^18 + 90x^16 + 300x^14 + 1425x^12 + 6875x^10 + 12625x^8 - 4375x^6 - 21250x^4 + 6250x^2 + 3125	\( 2^{20}\cdot 5^{15}\cdot 3319^{4} \)	20T755	Trivial (GRH)
20.8.3883103693091872000000000000000.2	x^20 - 10x^18 + 15x^16 + 125x^14 - 600x^12 + 875x^10 + 2625x^8 - 8125x^6 + 7500x^4 - 6250x^2 + 3125	\( 2^{20}\cdot 5^{15}\cdot 3319^{4} \)	20T755	Trivial (GRH)
20.12.3883103693091872000000000000000.3	x^20 - 15x^18 + 35x^16 + 100x^14 + 300x^12 - 3750x^10 + 9875x^8 - 18750x^6 + 29375x^4 - 21875x^2 + 3125	\( 2^{20}\cdot 5^{15}\cdot 3319^{4} \)	20T755	Trivial (GRH)
20.4.3883103693091872000000000000000.3	x^20 + 5x^18 - 45x^16 + 50x^14 + 1200x^12 - 1500x^10 - 13500x^8 - 11875x^6 - 5625x^4 - 15625x^2 + 3125	\( 2^{20}\cdot 5^{15}\cdot 3319^{4} \)	20T755	Trivial (GRH)
20.8.3883103693091872000000000000000.3	x^20 - 15x^18 + 95x^16 - 300x^14 + 200x^12 + 1750x^10 - 6250x^8 + 10625x^6 - 6875x^4 - 3125x^2 + 3125	\( 2^{20}\cdot 5^{15}\cdot 3319^{4} \)	20T755	Trivial (GRH)
20.8.3883103693091872000000000000000.4	x^20 - 20x^18 + 145x^16 - 400x^14 - 150x^12 + 2625x^10 - 2375x^8 - 4375x^6 + 1875x^4 + 6250x^2 + 3125	\( 2^{20}\cdot 5^{15}\cdot 3319^{4} \)	20T755	Trivial (GRH)
20.12.30370161984698266419200000000000.1	x^20 + 8x^18 - 23x^16 - 188x^14 + 418x^12 + 1132x^10 - 3718x^8 + 2308x^6 + 1381x^4 - 1340x^2 + 5	\( 2^{32}\cdot 5^{11}\cdot 3469^{4} \)	20T755	Trivial (GRH)
20.12.30370161984698266419200000000000.2	x^20 - 14x^18 + 25x^16 + 304x^14 - 742x^12 - 1964x^10 + 2402x^8 + 2208x^6 - 2651x^4 + 490x^2 + 5	\( 2^{32}\cdot 5^{11}\cdot 3469^{4} \)	20T755	Trivial (GRH)
20.0.485922591755172262707200000000000.1	x^20 + 25x^18 + 247x^16 + 1290x^14 + 3953x^12 + 7365x^10 + 8267x^8 + 5270x^6 + 1641x^4 + 165x^2 + 5	\( 2^{36}\cdot 5^{11}\cdot 3469^{4} \)	20T755	$[170]$ (GRH)
20.20.485922591755172262707200000000000.1	x^20 - 25x^18 + 247x^16 - 1290x^14 + 3953x^12 - 7365x^10 + 8267x^8 - 5270x^6 + 1641x^4 - 165x^2 + 5	\( 2^{36}\cdot 5^{11}\cdot 3469^{4} \)	20T755	Trivial (GRH)
20.0.12148064793879306567680000000000000.1	x^20 + 31x^18 + 377x^16 + 2334x^14 + 8121x^12 + 16595x^10 + 20235x^8 + 14700x^6 + 6175x^4 + 1375x^2 + 125	\( 2^{36}\cdot 5^{13}\cdot 3469^{4} \)	20T755	$[2, 432]$ (GRH)
20.20.12148064793879306567680000000000000.1	x^20 - 37x^18 + 529x^16 - 3908x^14 + 16421x^12 - 40265x^10 + 57035x^8 - 45450x^6 + 18925x^4 - 3375x^2 + 125	\( 2^{36}\cdot 5^{13}\cdot 3469^{4} \)	20T755	Trivial (GRH)