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 28 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.12.336186938823068443362886656.1	x^20 - 8x^18 + 9x^16 + 49x^14 - 84x^12 - 43x^10 + 124x^8 - 35x^6 - 17x^4 + 4x^2 + 1	\( 2^{10}\cdot 3^{10}\cdot 11^{18} \)	20T262	Trivial (GRH)
20.8.336186938823068443362886656.1	x^20 + 5x^18 - 8x^16 - 51x^14 + 9x^12 + 133x^10 + 49x^8 - 63x^6 - 18x^4 + 9x^2 + 1	\( 2^{10}\cdot 3^{10}\cdot 11^{18} \)	20T262	Trivial (GRH)
20.8.336186938823068443362886656.2	x^20 + 15x^18 + 82x^16 + 185x^14 + 80x^12 - 274x^10 - 249x^8 + 93x^6 + 53x^4 - 19x^2 + 1	\( 2^{10}\cdot 3^{10}\cdot 11^{18} \)	20T262	Trivial (GRH)
20.0.3084067808306675532115738624.1	x^20 - 18x^18 + 170x^16 - 1025x^14 + 4073x^12 - 10669x^10 + 18165x^8 - 19421x^6 + 12197x^4 - 3979x^2 + 529	\( 2^{20}\cdot 11^{18}\cdot 23^{2} \)	20T262	Trivial (GRH)
20.0.3084067808306675532115738624.2	x^20 - 19x^18 + 152x^16 - 710x^14 + 2248x^12 - 5004x^10 + 7989x^8 - 8956x^6 + 6781x^4 - 2944x^2 + 529	\( 2^{20}\cdot 11^{18}\cdot 23^{2} \)	20T262	Trivial (GRH)
20.8.10779662339431083287111532544.1	x^20 - 6x^19 + 8x^18 + 10x^17 - 9x^16 - 72x^15 + 178x^14 - 130x^13 - 431x^12 + 924x^11 + 100x^10 - 682x^9 - 1029x^8 + 1158x^7 + 1008x^6 - 1534x^5 - 408x^4 + 2346x^3 - 1904x^2 + 516x - 43	\( 2^{20}\cdot 11^{18}\cdot 43^{2} \)	20T262	Trivial (GRH)
20.8.10779662339431083287111532544.2	x^20 - 2x^19 + x^18 + 4x^17 - 11x^16 - 12x^15 - 9x^14 + 54x^13 - 15x^12 + 188x^10 + 88x^9 - 179x^8 - 412x^7 - 69x^6 - 56x^5 + 165x^4 + 58x^3 + 104x^2 + 14x - 43	\( 2^{20}\cdot 11^{18}\cdot 43^{2} \)	20T262	Trivial (GRH)
20.8.26099879633934179709805920256.1	x^20 - 2x^19 + 3x^18 - 4x^17 - 5x^16 - 12x^15 - 71x^14 + 90x^13 + 43x^12 + 86x^11 + 132x^10 - 10x^9 + 1249x^8 + 892x^7 - 1683x^6 - 1306x^5 + 639x^4 + 642x^3 - 20x^2 - 112x - 23	\( 2^{30}\cdot 11^{16}\cdot 23^{2} \)	20T262	Trivial (GRH)
20.8.26099879633934179709805920256.2	x^20 - 8x^19 + 26x^18 - 36x^17 - 57x^16 + 380x^15 - 800x^14 + 564x^13 + 1123x^12 - 2768x^11 + 1408x^10 + 2160x^9 - 2662x^8 - 764x^7 + 1652x^6 + 324x^5 - 467x^4 - 140x^3 + 28x^2 + 12x + 1	\( 2^{30}\cdot 11^{16}\cdot 23^{2} \)	20T262	Trivial (GRH)
20.12.46179397182603358960092184576.1	x^20 - 24x^18 - 22x^17 + 213x^16 + 396x^15 - 679x^14 - 2442x^13 - 644x^12 + 5456x^11 + 7041x^10 - 1122x^9 - 8692x^8 - 5984x^7 + 1115x^6 + 3806x^5 + 2423x^4 + 814x^3 + 170x^2 + 22x + 1	\( 2^{20}\cdot 11^{18}\cdot 89^{2} \)	20T262	Trivial (GRH)
20.12.344255425354822086003595935744.1	x^20 - 2x^18 - 18x^16 + 36x^14 + 82x^12 - 131x^10 - 145x^8 + 114x^6 + 47x^4 - 17x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T262	Trivial (GRH)
20.16.344255425354822086003595935744.1	x^20 - 13x^18 + 59x^16 - 96x^14 - 39x^12 + 287x^10 - 310x^8 + 125x^6 - 8x^4 - 6x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T262	Trivial (GRH)
20.4.344255425354822086003595935744.1	x^20 + 16x^18 + 91x^16 + 235x^14 + 262x^12 + 23x^10 - 204x^8 - 173x^6 - 51x^4 - 2x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T262	$[2]$ (GRH)
20.12.344255425354822086003595935744.2	x^20 - 2x^18 - 29x^16 + 58x^14 + 71x^12 - 164x^10 - 24x^8 + 114x^6 - 19x^4 - 6x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T262	Trivial (GRH)
20.16.344255425354822086003595935744.2	x^20 - 13x^18 + 48x^16 + 3x^14 - 314x^12 + 430x^10 + 64x^8 - 238x^6 + 102x^4 - 17x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T262	Trivial (GRH)
20.4.344255425354822086003595935744.2	x^20 + 14x^18 + 64x^16 + 93x^14 - 51x^12 - 230x^10 - 140x^8 + 42x^6 + 60x^4 + 15x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T262	$[2]$ (GRH)
20.12.344255425354822086003595935744.3	x^20 - 7x^18 + 5x^16 + 42x^14 - 63x^12 - 43x^10 + 92x^8 + 5x^6 - 35x^4 + 3x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T262	Trivial (GRH)
20.12.344255425354822086003595935744.4	x^20 + x^18 - 21x^16 - 10x^14 + 133x^12 + x^10 - 230x^8 + 111x^6 + 12x^4 - 10x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T262	Trivial (GRH)
20.12.344255425354822086003595935744.5	x^20 - 2x^18 - 18x^16 + 47x^14 + 49x^12 - 230x^10 + 196x^8 - 18x^6 - 30x^4 + 5x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T262	Trivial (GRH)
20.12.344255425354822086003595935744.6	x^20 - 6x^18 - 8x^16 + 92x^14 - 57x^12 - 307x^10 + 269x^8 + 256x^6 - 172x^4 - 2x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T262	Trivial (GRH)
20.12.470525233802978928640000000000.1	x^20 - 3x^18 - 16x^16 + 66x^14 + 15x^12 - 334x^10 + 423x^8 - 44x^6 - 144x^4 + 24x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T262	Trivial (GRH)
20.12.470525233802978928640000000000.2	x^20 - 5x^18 - 31x^16 + 165x^14 - 2x^12 - 532x^10 + 78x^8 + 286x^6 - 36x^4 - 34x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T262	Trivial (GRH)
20.12.13047078908784463218470268232704.1	x^20 - 8x^19 + 19x^18 + 21x^17 - 308x^16 + 760x^15 + 157x^14 - 3622x^13 + 6324x^12 - 1232x^11 - 9503x^10 + 5610x^9 + 9118x^8 + 4815x^7 - 36704x^6 + 34046x^5 - 583x^4 - 20406x^3 + 15804x^2 - 4705x + 397	\( 2^{10}\cdot 3^{10}\cdot 11^{18}\cdot 197^{2} \)	20T262	Trivial (GRH)
20.4.13047078908784463218470268232704.1	x^20 - 4x^19 + 15x^18 - 45x^17 + 176x^16 - 351x^15 + 986x^14 - 1855x^13 + 3013x^12 - 1804x^11 - 4927x^10 + 22627x^9 - 56057x^8 + 95198x^7 - 123380x^6 + 123377x^5 - 107107x^4 + 82114x^3 - 44238x^2 + 13581x - 1583	\( 2^{10}\cdot 3^{10}\cdot 11^{18}\cdot 197^{2} \)	20T262	$[2]$ (GRH)
20.12.14609322487882432594514132598784.1	x^20 - 2x^19 - 16x^18 + 28x^17 + 198x^16 - 472x^15 - 1311x^14 + 5264x^13 - 511x^12 - 20284x^11 + 25444x^10 + 16852x^9 - 54492x^8 + 30268x^7 + 11892x^6 - 21570x^5 + 10274x^4 - 1736x^3 - 147x^2 + 56x + 1	\( 2^{20}\cdot 11^{18}\cdot 1583^{2} \)	20T262	Trivial (GRH)
20.4.14609322487882432594514132598784.1	x^20 - 2x^19 + 8x^18 - 2x^17 + 58x^16 - 80x^15 + 359x^14 - 48x^13 + 432x^12 + 946x^11 + 243x^10 + 1166x^9 + 1489x^8 + 2412x^7 - 694x^6 - 184x^5 + 727x^4 - 1200x^3 + 171x^2 - 126x - 43	\( 2^{20}\cdot 11^{18}\cdot 1583^{2} \)	20T262	Trivial (GRH)
20.20.12569066605710630176407970532818944.1	x^20 - 4x^19 - 56x^18 + 160x^17 + 1170x^16 - 2560x^15 - 12444x^14 + 21818x^13 + 74182x^12 - 109934x^11 - 249732x^10 + 338096x^9 + 438377x^8 - 612082x^7 - 292220x^6 + 552758x^5 - 59820x^4 - 128586x^3 + 37814x^2 + 3666x - 1583	\( 2^{30}\cdot 11^{18}\cdot 1451^{2} \)	20T262	Trivial (GRH)
20.20.12569066605710630176407970532818944.2	x^20 - 2x^19 - 58x^18 + 86x^17 + 1411x^16 - 1312x^15 - 18748x^14 + 7872x^13 + 146699x^12 - 2200x^11 - 686190x^10 - 175274x^9 + 1918052x^8 + 779496x^7 - 3153426x^6 - 1467848x^5 + 2874345x^4 + 1298692x^3 - 1234282x^2 - 447034x + 150173	\( 2^{30}\cdot 11^{18}\cdot 1451^{2} \)	20T262	Trivial (GRH)