Global number field search results

Further refine search

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 1798)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.512192024001.1	x^12 - 2x^9 - 5x^7 + 14x^6 - 4x^4 - 16x^3 + 19x^2 - 7x + 1	\( 3^{6}\cdot 7^{3}\cdot 127^{3} \)	12T235	Trivial
12.0.1503878460993.1	x^12 - 2x^11 - 4x^10 + 6x^9 + 9x^8 - 3x^7 - 13x^6 - 9x^5 + 6x^4 + 13x^3 + 10x^2 + 4x + 1	\( 3^{6}\cdot 19^{3}\cdot 67^{3} \)	12T235	Trivial
12.4.3120193265625.1	x^12 - 3x^11 + 9x^9 - 5x^8 - 12x^7 + 7x^6 + 12x^5 - 5x^4 - 9x^3 + 3x + 1	\( 3^{2}\cdot 5^{6}\cdot 281^{3} \)	12T235	Trivial
12.0.7023616000000.1	x^12 - 2x^11 + 2x^10 - 4x^9 + 6x^8 - 6x^7 + 9x^6 - 18x^5 + 25x^4 - 18x^3 + 7x^2 - 2x + 1	\( 2^{16}\cdot 5^{6}\cdot 19^{3} \)	12T235	Trivial
12.4.13508516000000.1	x^12 - 2x^11 + 3x^10 - 2x^9 - x^8 - 6x^7 + 3x^6 - 2x^4 + 18x^3 + 4x^2 - 8x - 4	\( 2^{8}\cdot 5^{6}\cdot 7^{2}\cdot 41^{3} \)	12T235	Trivial
12.6.13907109998592.1	x^12 - 3x^10 - 4x^9 + 14x^7 + 2x^6 - 18x^5 + 5x^4 + 10x^3 - 5x^2 - 2x + 1	\( -\,2^{12}\cdot 3^{6}\cdot 167^{3} \)	12T235	Trivial
12.2.24325979359375.1	x^12 - 2x^11 + 4x^10 - 3x^9 - x^8 + 5x^7 - 9x^6 + 5x^5 - 11x^4 - 3x^3 + 4x^2 - 12x - 9	\( -\,5^{6}\cdot 19^{3}\cdot 61^{3} \)	12T235	Trivial
12.6.24325979359375.1	x^12 - x^11 - 4x^10 + 6x^9 + 3x^8 - 16x^7 + 9x^6 + 15x^5 - 20x^4 + 7x^3 + 6x^2 - 6x + 1	\( -\,5^{6}\cdot 19^{3}\cdot 61^{3} \)	12T235	Trivial
12.2.24325979359375.2	x^12 - 3x^11 + 3x^10 - 7x^8 + 21x^7 - 37x^6 + 39x^5 - 21x^4 + 9x^3 - 8x^2 + 3x - 1	\( -\,5^{6}\cdot 19^{3}\cdot 61^{3} \)	12T235	Trivial
12.0.33143899433125.1	x^12 - 4x^11 + 7x^10 - 6x^9 + x^8 + 7x^7 - 11x^6 + 7x^5 + x^4 - 6x^3 + 7x^2 - 4x + 1	\( 5^{4}\cdot 13^{3}\cdot 17^{6} \)	12T235	Trivial
12.6.47784725839872.1	x^12 - 6x^10 + 9x^8 + 2x^6 - 6x^4 - 7	\( -\,2^{18}\cdot 3^{12}\cdot 7^{3} \)	12T235	Trivial
12.2.167504391438336.1	x^12 - 2x^11 + 3x^10 + x^8 + 2x^7 - 3x^6 + 8x^5 - 10x^4 + 8x^3 - 4x^2 - 8	\( -\,2^{22}\cdot 3^{4}\cdot 79^{3} \)	12T235	Trivial
12.6.176836992750000.1	x^12 - 3x^10 - x^9 - 12x^7 - 40x^6 - 63x^5 - 51x^4 - 8x^3 + 18x^2 + 9x + 1	\( -\,2^{4}\cdot 3^{12}\cdot 5^{6}\cdot 11^{3} \)	12T235	Trivial
12.0.300578991243264.1	x^12 - 2x^10 + 29x^8 - 8x^6 + 18x^4 - 12x^2 + 6	\( 2^{37}\cdot 3^{7} \)	12T235	Trivial
12.0.1141260857376768.1	x^12 - 6x^10 + 15x^8 - 20x^6 + 24x^4 - 12x^2 + 2	\( 2^{31}\cdot 3^{12} \)	12T235	Trivial
12.0.1141260857376768.16	x^12 - 6x^10 + 9x^8 + 8x^6 - 24x^4 + 32	\( 2^{31}\cdot 3^{12} \)	12T235	Trivial
12.0.1202315964973056.1	x^12 - 2x^10 + 5x^8 + 16x^6 - 6x^4 - 12x^2 + 6	\( 2^{39}\cdot 3^{7} \)	12T235	Trivial
12.0.1202315964973056.2	x^12 + 8x^8 - 20x^6 + 21x^4 - 12x^2 + 6	\( 2^{39}\cdot 3^{7} \)	12T235	$[2]$
12.4.1672219746893824.1	x^12 - 2x^11 - 7x^10 + 12x^9 + 40x^8 - 68x^7 - 34x^6 + 144x^5 - 119x^4 + 14x^3 + 21x^2 - 12x + 2	\( 2^{37}\cdot 23^{3} \)	12T235	Trivial
12.4.1672219746893824.2	x^12 - 2x^11 - 7x^10 + 20x^9 + 10x^8 - 36x^7 - 42x^6 + 80x^5 - 5x^4 - 30x^3 + 11x^2 + 4x + 4	\( 2^{37}\cdot 23^{3} \)	12T235	Trivial
12.4.1672219746893824.3	x^12 - 4x^10 - 4x^6 + 45x^4 - 88x^2 + 46	\( 2^{37}\cdot 23^{3} \)	12T235	Trivial
12.4.1672219746893824.4	x^12 - 2x^10 + 17x^8 - 88x^6 + 86x^4 - 76x^2 + 46	\( 2^{37}\cdot 23^{3} \)	12T235	Trivial
12.4.1672219746893824.5	x^12 - 12x^10 + 36x^8 - 12x^6 - 91x^4 + 46	\( 2^{37}\cdot 23^{3} \)	12T235	Trivial
12.0.2705210921189376.1	x^12 - 2x^11 + x^10 - 2x^9 - 9x^8 - 4x^7 + 10x^6 + 28x^5 + 71x^4 + 126x^3 + 161x^2 + 126x + 41	\( 2^{37}\cdot 3^{9} \)	12T235	Trivial
12.0.2742118830047232.2	x^12 - 6x^11 + 15x^10 - 6x^9 - 18x^8 + 18x^7 + 51x^6 + 54x^5 + 72x^4 + 66x^3 + 45x^2 + 18x + 3	\( 2^{18}\cdot 3^{21} \)	12T235	Trivial
12.0.2742118830047232.3	x^12 - 12x^10 + 54x^8 - 108x^6 + 108x^4 - 144x^2 + 192	\( 2^{18}\cdot 3^{21} \)	12T235	Trivial
12.0.3043362286338048.3	x^12 + 2x^10 + 19x^8 + 20x^6 + 21x^4 + 6x^2 + 3	\( 2^{34}\cdot 3^{11} \)	12T235	Trivial
12.0.3043362286338048.4	x^12 - 2x^8 - 4x^6 + 9x^4 - 12x^2 + 12	\( 2^{34}\cdot 3^{11} \)	12T235	Trivial
12.0.3043362286338048.9	x^12 + 4x^10 + 14x^8 + 24x^6 + 51x^4 + 12x^2 + 108	\( 2^{34}\cdot 3^{11} \)	12T235	Trivial
12.4.3423782572130304.2	x^12 - 6x^10 - 9x^8 + 12x^4 + 12x^2 + 6	\( 2^{31}\cdot 3^{13} \)	12T235	Trivial
12.4.3423782572130304.3	x^12 - 6x^8 + 30x^4 - 48x^2 + 24	\( 2^{31}\cdot 3^{13} \)	12T235	Trivial
12.0.4565043429507072.5	x^12 - 6x^10 + 27x^8 - 56x^6 + 96x^4 - 12x^2 + 2	\( 2^{33}\cdot 3^{12} \)	12T235	Trivial
12.0.4565043429507072.6	x^12 - 6x^10 + 24x^8 - 20x^6 + 9x^4 - 6x^2 + 2	\( 2^{33}\cdot 3^{12} \)	12T235	Trivial
12.0.4565043429507072.13	x^12 - 6x^10 + 12x^8 + 16x^6 + 9x^4 + 6x^2 + 2	\( 2^{33}\cdot 3^{12} \)	12T235	Trivial (GRH)
12.0.4565043429507072.26	x^12 + 18x^8 - 8x^6 + 90x^4 - 48x^2 + 32	\( 2^{33}\cdot 3^{12} \)	12T235	Trivial
12.0.4809263859892224.4	x^12 - 4x^10 + 4x^8 + 4x^6 - 9x^4 + 6	\( 2^{41}\cdot 3^{7} \)	12T235	Trivial
12.0.4809263859892224.5	x^12 - 6x^10 + 27x^8 - 32x^6 - 6x^4 + 12x^2 + 6	\( 2^{41}\cdot 3^{7} \)	12T235	Trivial
12.0.4809263859892224.6	x^12 + 2x^10 + 3x^8 - 8x^6 + 18x^4 + 12x^2 + 6	\( 2^{41}\cdot 3^{7} \)	12T235	Trivial
12.0.4809263859892224.8	x^12 - 4x^10 + 10x^8 + 4x^6 + 3x^4 + 24	\( 2^{41}\cdot 3^{7} \)	12T235	Trivial
12.4.6688878987575296.1	x^12 - 10x^10 + 41x^8 - 88x^6 + 110x^4 - 92x^2 + 46	\( 2^{39}\cdot 23^{3} \)	12T235	Trivial
12.4.6688878987575296.2	x^12 + 2x^10 + 9x^8 - 8x^6 - 50x^4 - 4x^2 + 46	\( 2^{39}\cdot 23^{3} \)	12T235	Trivial
12.4.6688878987575296.3	x^12 - 14x^10 + 81x^8 - 256x^6 + 472x^4 - 464x^2 + 184	\( 2^{39}\cdot 23^{3} \)	12T235	Trivial
12.4.6688878987575296.4	x^12 - 12x^10 + 62x^8 - 188x^6 + 361x^4 - 400x^2 + 184	\( 2^{39}\cdot 23^{3} \)	12T235	Trivial
12.4.6688878987575296.5	x^12 - 8x^10 + 26x^8 - 64x^6 + 108x^4 - 96x^2 + 184	\( 2^{39}\cdot 23^{3} \)	12T235	Trivial
12.4.6688878987575296.6	x^12 - 4x^10 + 10x^8 - 44x^6 + 41x^4 + 184	\( 2^{39}\cdot 23^{3} \)	12T235	Trivial
12.4.6884340550074368.3	x^12 - 8x^10 + 18x^8 - 34x^6 + 41x^4 - 34x^2 + 17	\( 2^{24}\cdot 17^{7} \)	12T235	Trivial
12.8.7214229398265625.1	x^12 - x^11 - 9x^10 + 10x^9 + 18x^8 - 47x^7 + 4x^6 + 64x^5 - 63x^4 - 32x^3 + 26x^2 + x - 1	\( 5^{6}\cdot 59^{3}\cdot 131^{3} \)	12T235	Trivial
12.4.7214229398265625.1	x^12 - 3x^11 + 3x^10 + 10x^9 - 42x^8 + 66x^7 - 61x^6 + 20x^5 - 5x^4 - 12x^3 + 19x^2 - 30x + 5	\( 5^{6}\cdot 59^{3}\cdot 131^{3} \)	12T235	Trivial
12.8.7214229398265625.2	x^12 - 3x^11 - 3x^10 + 9x^9 + 20x^8 - 9x^7 - 148x^6 - 38x^5 + 301x^4 + 223x^3 + x^2 - 14x + 1	\( 5^{6}\cdot 59^{3}\cdot 131^{3} \)	12T235	Trivial
12.4.7214229398265625.2	x^12 - 3x^11 + 11x^10 - 10x^9 - 10x^8 + 32x^7 - 52x^6 + 71x^5 - 30x^4 - 80x^3 + 136x^2 - 84x + 19	\( 5^{6}\cdot 59^{3}\cdot 131^{3} \)	12T235	Trivial