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 2125)

Label	Polynomial	Discriminant	Galois group	Class group
10.4.4930254263.1	x^10 - 3x^9 + 2x^8 + 3x^7 - 9x^6 + 11x^5 - 9x^4 + 3x^3 + 2x^2 - 3x + 1	\( -\,11^{8}\cdot 23 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.4.9217431883.1	x^10 - 2x^9 + 5x^7 - 12x^6 + 15x^5 - 12x^4 + 5x^3 - 2x + 1	\( -\,11^{8}\cdot 43 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.4.14362045027.1	x^10 - 3x^9 + x^8 + x^7 + 9x^6 - 18x^5 + 5x^4 + 9x^3 - 6x^2 - x + 1	\( -\,11^{8}\cdot 67 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.2.19077940409.1	x^10 - 4x^9 + 7x^8 - 11x^7 + 14x^6 - 15x^5 + 14x^4 - 11x^3 + 7x^2 - 4x + 1	\( 11^{8}\cdot 89 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.6.23365118029.1	x^10 - 3x^9 + x^8 + x^7 - 2x^6 + 4x^5 + 5x^4 - 2x^3 - 6x^2 - x + 1	\( 11^{8}\cdot 109 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.4.28081013411.1	x^10 - 5x^9 + 11x^8 - 14x^7 + 7x^6 + 7x^5 - 14x^4 + 10x^3 - 3x + 1	\( -\,11^{8}\cdot 131 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.6.42228699557.1	x^10 - x^9 - 5x^8 + 6x^7 + 8x^6 - 13x^5 - 6x^4 + 13x^3 + 4x^2 - 5x - 1	\( 11^{8}\cdot 197 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.4.42657417319.1	x^10 - 4x^9 + 6x^8 + x^7 - 15x^6 + 22x^5 - 12x^4 - 2x^3 + 8x^2 - 5x + 1	\( -\,11^{8}\cdot 199 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.6.51660490321.1	x^10 - 2x^9 - 3x^8 + 12x^7 - 7x^6 - 9x^5 + 17x^4 - 6x^3 - 6x^2 + 5x - 1	\( 11^{8}\cdot 241 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.6.54232796893.1	x^10 - 4x^9 + 5x^8 + 2x^7 - 8x^6 - x^5 + 4x^4 + 6x^3 - 2x^2 - 3x + 1	\( 11^{9}\cdot 23 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.4.56376385703.1	x^10 - x^9 + 2x^7 + 2x^6 - 4x^5 - 5x^4 + 7x^3 - 4x + 1	\( -\,11^{8}\cdot 263 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.4.65808176467.1	x^10 - x^9 - 3x^8 + x^6 - 4x^5 - 2x^4 + 11x^3 + 13x^2 + 6x + 1	\( -\,11^{8}\cdot 307 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.8.70952789611.1	x^10 - x^9 - 6x^8 + 9x^7 + 5x^6 - 18x^5 + 9x^4 + 12x^3 - 10x^2 - 3x + 1	\( -\,11^{8}\cdot 331 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.6.75668684993.1	x^10 - 2x^9 - x^8 + 11x^7 - 17x^6 + 4x^5 + 15x^4 - 11x^3 - 5x^2 + 3x + 1	\( 11^{8}\cdot 353 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.2.79955862613.1	x^10 - x^9 + 2x^8 - 4x^7 + 3x^6 - 2x^5 - 3x^4 - 15x^3 - 2x^2 - x - 1	\( 11^{8}\cdot 373 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.6.85100475757.1	x^10 - x^9 + 2x^7 - 9x^6 + 18x^5 - 27x^4 + 18x^3 - 4x + 1	\( 11^{8}\cdot 397 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.4.89816371139.1	x^10 - x^9 + 2x^8 - 4x^7 + 3x^6 - 2x^5 - 3x^4 + 18x^3 - 24x^2 + 10x - 1	\( -\,11^{8}\cdot 419 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.4.94103548759.1	x^10 - 5x^9 + 16x^8 - 34x^7 + 51x^6 - 55x^5 + 37x^4 - 12x^3 - 5x^2 + 6x - 1	\( -\,11^{8}\cdot 439 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.6.98819444141.1	x^10 - x^9 - x^8 + 5x^7 - 5x^6 - 11x^5 - 3x^4 - 7x^3 - 4x^2 + 2x + 1	\( 11^{8}\cdot 461 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.4.99248161903.1	x^10 - 2x^9 + 2x^8 - 7x^7 + 18x^6 - 31x^5 + 23x^4 - 8x^3 + x^2 + 3x - 1	\( -\,11^{8}\cdot 463 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.6.101391750713.1	x^10 - 4x^9 + 5x^8 + 2x^7 - 19x^6 + 32x^5 - 18x^4 - 16x^3 + 31x^2 - 14x + 1	\( 11^{9}\cdot 43 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.4.122398921051.1	x^10 - 5x^9 + 13x^8 - 22x^7 + 20x^6 - 4x^5 - 10x^4 + 11x^3 - 3x^2 - x + 1	\( -\,11^{8}\cdot 571 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.2.127114816433.1	x^10 - 2x^9 + 2x^8 + 4x^7 - 4x^6 + 13x^5 + x^4 + 14x^3 + x^2 + 3x - 1	\( 11^{8}\cdot 593 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.2.132259429577.1	x^10 - 3x^9 + 5x^8 - 2x^7 - x^6 + 15x^5 - 6x^4 + 16x^3 + 2x^2 + 6x - 1	\( 11^{8}\cdot 617 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.4.141262502579.1	x^10 - 2x^9 + x^8 - x^7 + 7x^6 - 15x^5 + 15x^4 - 12x^3 - x^2 + 9x - 1	\( -\,11^{8}\cdot 659 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.6.141691220341.1	x^10 - 2x^9 - x^8 - 6x^6 + 15x^5 - 7x^4 - 11x^3 + 17x^2 - 8x + 1	\( 11^{8}\cdot 661 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.8.146407115723.1	x^10 - 2x^9 - 4x^8 + 7x^7 - 3x^6 - 11x^5 + 17x^4 + 6x^3 - 12x^2 + x + 1	\( -\,11^{8}\cdot 683 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.8.155838906487.1	x^10 - 2x^9 - 3x^8 + 12x^7 - 7x^6 - 20x^5 + 17x^4 + 16x^3 - 6x^2 - 6x - 1	\( -\,11^{8}\cdot 727 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.6.157982495297.1	x^10 - 3x^9 - 2x^8 + 17x^7 - 18x^6 - 12x^5 + 36x^4 - 20x^3 - 6x^2 + 7x + 1	\( 11^{9}\cdot 67 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.2.164841979489.1	x^10 - x^9 + 4x^8 + x^7 + 5x^6 - 5x^5 - 3x^4 - 19x^3 - 16x^2 - 9x - 1	\( 11^{8}\cdot 769 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.6.183705561017.1	x^10 - x^9 - x^8 + 5x^7 - 16x^6 + 11x^5 + 19x^4 - 40x^3 + 29x^2 - 9x + 1	\( 11^{8}\cdot 857 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.8.184134278779.1	x^10 - 4x^9 - x^8 + 19x^7 - 13x^6 - 13x^5 - x^4 + 13x^3 + 4x^2 - 3x - 1	\( -\,11^{8}\cdot 859 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.6.188850174161.1	x^10 - 2x^9 - x^8 + 5x^6 - 7x^5 + 15x^4 - 16x^2 + 3x + 1	\( 11^{8}\cdot 881 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.8.202997860307.1	x^10 - 4x^9 - x^8 + 19x^7 - 13x^6 - 24x^5 + 32x^4 + 2x^3 - 18x^2 + 8x - 1	\( -\,11^{8}\cdot 947 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.4.207285037927.1	x^10 - x^9 + 3x^8 - 7x^7 + 8x^6 - 7x^5 - 13x^4 + 14x^3 - 15x^2 + 7x - 1	\( -\,11^{8}\cdot 967 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.8.209857344499.1	x^10 - 5x^9 + 3x^8 + 18x^7 - 24x^6 - 12x^5 + 27x^4 - 3x^3 - 7x^2 + 2x + 1	\( -\,11^{9}\cdot 89 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.2.212000933309.1	x^10 - 3x^9 + 2x^8 - 8x^7 + 2x^6 - 11x^5 + 2x^4 - 8x^3 + 2x^2 - 3x + 1	\( 11^{8}\cdot 23\cdot 43 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.6.212000933309.1	x^10 - 2x^9 - 3x^8 + x^7 + 15x^6 - 9x^5 - 16x^4 + 16x^3 + 5x^2 - 6x - 1	\( 11^{8}\cdot 23\cdot 43 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.6.212000933309.2	x^10 - 5x^9 + 7x^8 + 2x^7 - 16x^6 + 20x^5 - 8x^4 - 5x^3 + 5x^2 - x - 1	\( 11^{8}\cdot 23\cdot 43 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.6.212000933309.3	x^10 - x^9 - 7x^8 + 12x^7 - 6x^6 - 5x^5 + 19x^4 - 19x^3 + 6x^2 + 2x - 1	\( 11^{8}\cdot 23\cdot 43 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.6.212000933309.4	x^10 - x^9 - 6x^8 + 9x^7 - 6x^6 + 15x^5 - 13x^4 + x^3 + x^2 - 3x + 1	\( 11^{8}\cdot 23\cdot 43 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.8.212429651071.1	x^10 - 4x^9 + 3x^8 + 4x^7 - 7x^6 + 15x^5 - 19x^4 - 6x^3 + 20x^2 - 9x + 1	\( -\,11^{8}\cdot 991 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.6.217145546453.1	x^10 - 3x^9 + 10x^7 - 14x^6 - 4x^5 + 7x^4 + 8x^3 + 11x^2 + 6x + 1	\( 11^{8}\cdot 1013 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.4.219503494144.1	x^10 + 4x^8 + 2x^6 - 5x^4 - 2x^2 + 1	\( -\,2^{10}\cdot 11^{8} \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.8.219503494144.1	x^10 - 2x^8 - 5x^6 + 13x^4 - 7x^2 + 1	\( -\,2^{10}\cdot 11^{8} \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.4.219503494144.2	x^10 + x^8 - 4x^6 - 3x^4 + 3x^2 + 1	\( -\,2^{10}\cdot 11^{8} \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.6.221432724073.1	x^10 - 3x^9 + x^8 + 12x^7 - 13x^6 - 7x^5 + 16x^4 - 13x^3 - 6x^2 + 10x + 1	\( 11^{8}\cdot 1033 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.4.240725023363.1	x^10 - 4x^9 + 3x^8 + 4x^7 - 18x^6 + 26x^5 - 19x^4 + 5x^3 - 2x^2 + 2x + 1	\( -\,11^{8}\cdot 1123 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.4.254443991747.1	x^10 - 3x^9 + 4x^8 - 4x^7 - 3x^6 - 11x^5 + 31x^4 - 3x^3 + 13x^2 - x - 1	\( -\,11^{8}\cdot 1187 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.4.257016298319.1	x^10 - 5x^9 + 14x^8 - 26x^7 + 31x^6 - 23x^5 + 5x^4 + 8x^3 - 7x^2 + 2x + 1	\( -\,11^{9}\cdot 109 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial