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 74)

Label	Polynomial	Discriminant	Galois group	Class group
10.6.113395848049.1	x^10 - x^9 - 3x^8 + x^6 + 7x^5 - 2x^4 - 11x^3 + 2x^2 + 6x + 1	\( 11^{8}\cdot 23^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.2.113395848049.1	x^10 - 2x^9 - 6x^7 - x^6 - 7x^5 - x^4 - 6x^3 - 2x + 1	\( 11^{8}\cdot 23^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.2.219503494144.1	x^10 + 2x^8 - 5x^6 - 13x^4 - 7x^2 - 1	\( 2^{10}\cdot 11^{8} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.6.219503494144.1	x^10 - x^8 - 4x^6 + 3x^4 + 3x^2 - 1	\( 2^{10}\cdot 11^{8} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.6.219503494144.2	x^10 - 4x^8 + 2x^6 + 5x^4 - 2x^2 - 1	\( 2^{10}\cdot 11^{8} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.2.396349570969.1	x^10 - 3x^9 + 5x^8 - 13x^7 + 21x^6 - 18x^5 + 27x^4 - 17x^3 - 9x^2 + 6x - 23	\( 11^{8}\cdot 43^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.6.396349570969.1	x^10 - 4x^9 + x^8 + 6x^7 - 5x^6 + x^4 + 2x^3 + 8x^2 + 2x - 1	\( 11^{8}\cdot 43^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.2.962257016809.1	x^10 - 4x^9 + 13x^8 - 17x^7 + 20x^6 - x^5 - 22x^4 + 55x^3 - 55x^2 + 44x - 11	\( 11^{8}\cdot 67^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.6.962257016809.1	x^10 - 2x^9 - x^8 - 17x^6 + 4x^5 - 18x^4 + 17x^2 - 8x + 1	\( 11^{8}\cdot 67^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.6.1697936696401.1	x^10 - 4x^9 + 7x^8 - 11x^7 + 3x^6 + 18x^5 - 41x^4 + 33x^3 + 51x^2 - 15x + 1	\( 11^{8}\cdot 89^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.6.1697936696401.2	x^10 - x^9 + 2x^7 - 9x^6 + 7x^5 - 27x^4 - 26x^3 + 77x^2 + 18x + 1	\( 11^{8}\cdot 89^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.2.2546797865161.1	x^10 - 4x^9 + 11x^8 - 26x^7 + 39x^6 - 70x^5 + 57x^4 - 86x^3 + 44x^2 - 34x + 1	\( 11^{8}\cdot 109^{2} \)	$C_2^4 : C_5$ (as 10T8)	$[2]$
10.6.2546797865161.1	x^10 - 4x^9 - 4x^8 + 33x^7 - 30x^6 - 15x^5 - 8x^4 + 44x^3 + 40x^2 - 48x - 32	\( 11^{8}\cdot 109^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.2.3678612756841.1	x^10 - 3x^9 + 8x^8 - 18x^7 + 34x^6 - 78x^5 + 99x^4 - 143x^3 + 88x^2 - 88x + 11	\( 11^{8}\cdot 131^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.6.3678612756841.1	x^10 - 4x^9 + 4x^8 - 8x^7 + 13x^6 + 37x^5 - 63x^4 + 48x^3 - 102x^2 + 32x - 1	\( 11^{8}\cdot 131^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.2.7476806640625.1	x^10 - 10x^7 - 5x^6 + 19x^5 + 25x^4 - 20x^3 - 10x - 7	\( 5^{16}\cdot 7^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.6.7476806640625.1	x^10 - 10x^8 - 5x^7 + 30x^6 + 33x^5 - 45x^4 - 50x^3 + 25x^2 + 25x - 5	\( 5^{16}\cdot 7^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.2.8319053812729.1	x^10 - 4x^9 + 11x^8 - 15x^7 - 5x^6 + 84x^5 - 229x^4 + 409x^3 - 517x^2 + 439x - 197	\( 11^{8}\cdot 197^{2} \)	$C_2^4 : C_5$ (as 10T8)	$[2]$
10.6.8319053812729.1	x^10 - 2x^9 - 8x^8 + 31x^7 - 12x^6 - 99x^5 + 181x^4 - 94x^3 - 133x^2 + 235x - 89	\( 11^{8}\cdot 197^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.2.8488826046481.1	x^10 - 3x^9 + 6x^8 - 11x^7 + 4x^6 - 26x^5 + 16x^4 - 44x^3 + 10x^2 - 9x - 197	\( 11^{8}\cdot 199^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.6.8488826046481.1	x^10 - x^9 - 2x^8 - 14x^7 + 2x^6 + 44x^5 + 47x^4 + 7x^3 - 70x^2 - 80x - 23	\( 11^{8}\cdot 199^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.2.21322275936025.1	x^10 - 4x^9 + 7x^8 - 12x^7 + 35x^6 - 22x^5 - 2x^4 + 28x^3 + 3x^2 - 8x - 1	\( 5^{2}\cdot 31^{8} \)	$C_2^4 : C_5$ (as 10T8)	$[2]$
10.6.21322275936025.1	x^10 - 3x^9 - 7x^8 + 27x^7 + 16x^6 - 89x^5 - 55x^4 + 84x^3 + 105x^2 + 41x + 5	\( 5^{2}\cdot 31^{8} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.6.59986403617921.1	x^10 - 2x^9 - 17x^7 - x^6 + 4x^5 + 164x^4 + 280x^3 - 198x^2 - 497x - 197	\( 11^{8}\cdot 23^{4} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.2.71864327062089.1	x^10 - 4x^9 + x^8 + 22x^7 - 29x^6 - 26x^5 + 51x^4 - 28x^3 + 30x^2 - 18x - 27	\( 3^{2}\cdot 41^{8} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.6.71864327062089.1	x^10 + 10x^8 - x^6 - 43x^4 + 39x^2 - 9	\( 3^{2}\cdot 41^{8} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.10.116117348402176.1	x^10 - 20x^8 + 149x^6 - 519x^4 + 851x^2 - 529	\( 2^{10}\cdot 11^{8}\cdot 23^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.2.116117348402176.1	x^10 + 8x^8 - 14x^6 - 271x^4 - 736x^2 - 529	\( 2^{10}\cdot 11^{8}\cdot 23^{2} \)	$C_2^4 : C_5$ (as 10T8)	$[2, 2]$
10.6.116117348402176.1	x^10 - 12x^8 + 18x^6 + 135x^4 - 184x^2 - 529	\( 2^{10}\cdot 11^{8}\cdot 23^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.10.116117348402176.2	x^10 - 25x^8 + 206x^6 - 711x^4 + 1035x^2 - 529	\( 2^{10}\cdot 11^{8}\cdot 23^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.2.116117348402176.2	x^10 + 13x^8 + 6x^6 - 233x^4 - 667x^2 - 529	\( 2^{10}\cdot 11^{8}\cdot 23^{2} \)	$C_2^4 : C_5$ (as 10T8)	$[2]$
10.6.116117348402176.2	x^10 - 3x^8 - 47x^6 + 103x^4 + 276x^2 - 529	\( 2^{10}\cdot 11^{8}\cdot 23^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.2.116117348402176.3	x^10 + 17x^8 + 87x^6 + 78x^4 - 391x^2 - 529	\( 2^{10}\cdot 11^{8}\cdot 23^{2} \)	$C_2^4 : C_5$ (as 10T8)	$[2]$
10.6.116117348402176.3	x^10 - 9x^8 - 38x^6 + 163x^4 + 345x^2 - 529	\( 2^{10}\cdot 11^{8}\cdot 23^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.6.116117348402176.4	x^10 + 7x^8 - 75x^6 + 27x^4 + 460x^2 - 529	\( 2^{10}\cdot 11^{8}\cdot 23^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.6.116117348402176.5	x^10 + 2x^8 - 71x^6 + 42x^4 + 598x^2 - 529	\( 2^{10}\cdot 11^{8}\cdot 23^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.6.156250000000000.1	x^10 - 10x^6 - 5x^4 + 10x^2 - 1	\( 2^{10}\cdot 5^{16} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.2.156250000000000.1	x^10 + 5x^8 - 5x^6 - 25x^4 - 10x^2 - 1	\( 2^{10}\cdot 5^{16} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.6.156250000000000.2	x^10 - 5x^8 - 15x^6 + 15x^4 + 30x^2 - 1	\( 2^{10}\cdot 5^{16} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.10.209668923042601.1	x^10 - 4x^9 - 20x^8 + 71x^7 + 174x^6 - 419x^5 - 792x^4 + 792x^3 + 1496x^2 - 352	\( 11^{8}\cdot 23^{2}\cdot 43^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.6.366363525390625.1	x^10 - 5x^9 - 5x^8 + 30x^7 - 5x^6 - 25x^5 + 50x^4 + 5x^3 - 160x^2 + 20x + 101	\( 5^{16}\cdot 7^{4} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.10.405861960672256.1	x^10 - 25x^8 + 239x^6 - 1085x^4 + 2322x^2 - 1849	\( 2^{10}\cdot 11^{8}\cdot 43^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.10.405861960672256.2	x^10 - 27x^8 + 274x^6 - 1275x^4 + 2623x^2 - 1849	\( 2^{10}\cdot 11^{8}\cdot 43^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.10.451311402416281.1	x^10 - 3x^9 - 27x^8 + 88x^7 + 191x^6 - 697x^5 - 468x^4 + 2013x^3 + 417x^2 - 1791x - 461	\( 11^{8}\cdot 1451^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.10.451311402416281.2	x^10 - 3x^9 - 29x^8 + 84x^7 + 283x^6 - 759x^5 - 1102x^4 + 2461x^3 + 1564x^2 - 2278x + 197	\( 11^{8}\cdot 1451^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.10.509033961891961.1	x^10 - 3x^9 - 27x^8 + 77x^7 + 246x^6 - 631x^5 - 886x^4 + 1716x^3 + 1352x^2 - 1120x - 736	\( 11^{8}\cdot 23^{2}\cdot 67^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.6.533056898400625.1	x^10 - 4x^9 - 7x^8 + 8x^7 + 43x^6 + 131x^5 + 41x^4 + 40x^3 - 148x^2 + 55x - 5	\( 5^{4}\cdot 31^{8} \)	$C_2^4 : C_5$ (as 10T8)	Trivial
10.10.537159561950209.1	x^10 - x^9 - 35x^8 + 30x^7 + 409x^6 - 319x^5 - 1988x^4 + 1503x^3 + 3648x^2 - 2698x - 1013	\( 11^{8}\cdot 1583^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial (GRH)
10.10.537159561950209.2	x^10 - x^9 - 36x^8 + 33x^7 + 441x^6 - 367x^5 - 2114x^4 + 1540x^3 + 3544x^2 - 1952x - 736	\( 11^{8}\cdot 1583^{2} \)	$C_2^4 : C_5$ (as 10T8)	Trivial (GRH)
10.6.646778943558801.1	x^10 - 4x^9 - 6x^8 + 69x^7 - 193x^6 + 282x^5 - 220x^4 + 54x^3 + 54x^2 - 45x + 9	\( 3^{4}\cdot 41^{8} \)	$C_2^4 : C_5$ (as 10T8)	Trivial