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 7174)

Label	Polynomial	Discriminant	Galois group	Class group
16.8.2528149687744140625.1	x^16 - 5x^15 + 6x^14 + 17x^13 - 68x^12 + 84x^11 + 22x^10 - 225x^9 + 352x^8 - 237x^7 - 82x^6 + 347x^5 - 379x^4 + 251x^3 - 92x^2 + 8x + 1	\( 5^{12}\cdot 11^{4}\cdot 29^{4} \)	$D_4^2.C_2$ (as 16T388)	Trivial (GRH)
16.8.2624400000000000000.1	x^16 - 8x^15 + 29x^14 - 58x^13 + 48x^12 + 62x^11 - 234x^10 + 306x^9 - 172x^8 - 68x^7 + 239x^6 - 314x^5 + 313x^4 - 206x^3 + 76x^2 - 14x + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{14} \)	$(C_8:C_2):C_2$ (as 16T16)	Trivial
16.8.3074049931884765625.1	x^16 - 5x^14 + 4x^12 + 15x^10 - 49x^8 + 60x^6 - 26x^4 + 1	\( 5^{12}\cdot 11^{2}\cdot 101^{4} \)	16T1174	Trivial
16.8.3267434519824695296.1	x^16 - 4x^15 + 8x^14 - 14x^13 + 20x^12 - 22x^11 + 7x^10 + 18x^9 - 53x^8 + 86x^7 - 119x^6 + 58x^5 + 68x^4 - 42x^3 - 16x^2 + 4x + 1	\( 2^{24}\cdot 41^{7} \)	$C_4.D_4:C_4$ (as 16T289)	Trivial
16.8.3401878219828515625.1	x^16 - x^15 - 9x^14 - 4x^13 + 17x^12 + 28x^11 + 14x^10 - 23x^9 - 45x^8 - 23x^7 + 14x^6 + 28x^5 + 17x^4 - 4x^3 - 9x^2 - x + 1	\( 5^{8}\cdot 11^{4}\cdot 29^{6} \)	$C_4.C_2^2:D_4$ (as 16T211)	Trivial (GRH)
16.8.4577583207890700225.1	x^16 - 20x^12 + 46x^10 - 10x^8 - 76x^6 + 93x^4 - 34x^2 + 1	\( 3^{10}\cdot 5^{2}\cdot 1327^{4} \)	16T1664	Trivial (GRH)
16.8.4635236761600000000.1	x^16 - 2x^15 - 2x^14 - 4x^13 + 35x^12 - 44x^11 - 22x^10 + 174x^9 - 331x^8 + 302x^7 - 62x^6 - 188x^5 + 259x^4 - 150x^3 + 34x^2 + 2x - 1	\( 2^{24}\cdot 5^{8}\cdot 29^{4} \)	$D_4^2.C_2$ (as 16T388)	Trivial (GRH)
16.8.4635236761600000000.2	x^16 - 2x^15 - 8x^14 + 26x^13 - 19x^12 - 4x^11 + 4x^10 - 16x^9 + 53x^8 - 56x^7 + 6x^6 + 54x^5 - 53x^4 + 6x^3 + 16x^2 - 8x + 1	\( 2^{24}\cdot 5^{8}\cdot 29^{4} \)	16T969	Trivial (GRH)
16.8.4635236761600000000.3	x^16 - 6x^15 + 14x^14 - 14x^13 - 17x^12 + 94x^11 - 184x^10 + 222x^9 - 167x^8 + 34x^7 + 74x^6 - 112x^5 + 135x^4 - 116x^3 + 54x^2 - 12x + 1	\( 2^{24}\cdot 5^{8}\cdot 29^{4} \)	16T969	Trivial (GRH)
16.8.4715518145963530689.1	x^16 - 4x^15 + 2x^14 + 18x^13 - 45x^12 + 10x^11 + 102x^10 - 112x^9 - 64x^8 + 156x^7 - 16x^6 - 89x^5 + 31x^4 + 24x^3 - 11x^2 - 3x + 1	\( 3^{8}\cdot 7^{2}\cdot 19^{4}\cdot 103^{4} \)	16T1664	Trivial (GRH)
16.8.4885218876572265625.1	x^16 - 2x^15 - 3x^14 + 3x^13 + x^12 + 5x^11 - 31x^10 + 6x^9 + 89x^8 + 6x^7 - 31x^6 + 5x^5 + x^4 + 3x^3 - 3x^2 - 2x + 1	\( 5^{10}\cdot 29^{8} \)	$C_4\wr C_2$ (as 16T42)	Trivial (GRH)
16.8.5692982583251953125.1	x^16 - 4x^15 + 4x^14 - x^13 - 3x^12 + 30x^11 - 40x^10 - 25x^9 + 63x^8 - 32x^7 + 4x^6 + 34x^5 - 46x^4 + 6x^3 + 17x^2 - 8x + 1	\( 3^{8}\cdot 5^{12}\cdot 59^{2}\cdot 1021 \)	16T1771	Trivial
16.8.5817627315785433088.1	x^16 - 2x^15 - 3x^14 + 2x^13 + x^12 + 14x^11 - 6x^10 + 4x^9 - 23x^8 + 4x^7 - 6x^6 + 14x^5 + x^4 + 2x^3 - 3x^2 - 2x + 1	\( 2^{24}\cdot 41^{6}\cdot 73 \)	16T1722	Trivial
16.8.6116053585556640625.1	x^16 - 7x^14 - x^13 + 9x^12 + 15x^11 - x^10 - 8x^9 - 17x^8 - 8x^7 - x^6 + 15x^5 + 9x^4 - x^3 - 7x^2 + 1	\( 5^{10}\cdot 29^{4}\cdot 941^{2} \)	16T1559	Trivial
16.8.6417946534267578125.1	x^16 - x^15 - 8x^14 + 13x^13 + 12x^12 - 39x^11 + 14x^10 + 24x^9 + 14x^8 - 67x^7 + 46x^6 + 13x^5 - 48x^4 + 36x^3 - 7x^2 - 3x + 1	\( 5^{10}\cdot 29^{5}\cdot 179^{2} \)	16T1702	Trivial
16.8.6636230027766015625.1	x^16 - 5x^15 + 6x^14 + 13x^13 - 43x^12 + 36x^11 - 19x^10 + 123x^9 - 266x^8 + 72x^7 + 421x^6 - 556x^5 + 197x^4 + 52x^3 - 34x^2 + 1	\( 5^{8}\cdot 13^{4}\cdot 29^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial (GRH)
16.8.6775050767527611461.1	x^16 - x^15 - 8x^14 + 3x^13 + 12x^12 - 8x^11 + 6x^10 + 13x^9 - 7x^8 + 13x^7 + 6x^6 - 8x^5 + 12x^4 + 3x^3 - 8x^2 - x + 1	\( 29\cdot 483345053^{2} \)	16T1948	Trivial
16.8.6775050767527611461.2	x^16 - x^15 - 8x^14 + 11x^13 + 12x^12 - 19x^11 - 5x^10 + 2x^9 + 15x^8 + 2x^7 - 5x^6 - 19x^5 + 12x^4 + 11x^3 - 8x^2 - x + 1	\( 29\cdot 483345053^{2} \)	16T1948	Trivial
16.8.6871947673600000000.1	x^16 - 4x^14 - 4x^12 - 36x^10 + 118x^8 - 188x^6 + 124x^4 - 28x^2 + 1	\( 2^{44}\cdot 5^{8} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial (GRH)
16.8.7092723713765801984.1	x^16 - 8x^15 + 34x^14 - 98x^13 + 203x^12 - 308x^11 + 331x^10 - 214x^9 + 9x^8 + 148x^7 - 159x^6 + 64x^5 + 16x^4 - 30x^3 + 9x^2 + 2x - 1	\( 2^{24}\cdot 41^{6}\cdot 89 \)	16T1722	Trivial
16.8.7444817979750390625.1	x^16 - 5x^15 + 4x^14 + 21x^13 - 48x^12 - 3x^11 + 118x^10 - 110x^9 - 81x^8 + 191x^7 - 51x^6 - 105x^5 + 79x^4 + 9x^3 - 23x^2 + x + 1	\( 5^{8}\cdot 29^{6}\cdot 179^{2} \)	16T1445	Trivial
16.8.7444817979750390625.2	x^16 - 3x^15 + 5x^13 - 6x^12 - 12x^11 + 20x^10 + 27x^9 - 36x^8 + 24x^7 + 72x^6 - 58x^5 - 87x^4 - 13x^3 + 11x^2 + 5x + 1	\( 5^{8}\cdot 29^{6}\cdot 179^{2} \)	16T876	Trivial (GRH)
16.8.7470129603273724489.1	x^16 - 8x^15 + 20x^14 - 71x^12 + 62x^11 + 102x^10 - 125x^9 - 102x^8 + 124x^7 + 82x^6 - 67x^5 - 44x^4 + 14x^3 + 13x^2 - x - 1	\( 59\cdot 419\cdot 17383253^{2} \)	16T1948	Trivial
16.8.7763680146828515625.1	x^16 - 5x^15 + 6x^14 + 4x^13 - 10x^12 + 7x^11 - 30x^10 + 46x^9 + 32x^8 - 112x^7 + 29x^6 + 85x^5 - 37x^4 - 29x^3 + 10x^2 + 3x - 1	\( 3^{4}\cdot 5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2} \)	16T1553	Trivial
16.8.7763680146828515625.2	x^16 - x^15 - 3x^14 + 3x^13 + 7x^12 + 12x^11 - 17x^10 - 40x^9 - 12x^8 + 21x^7 + 58x^6 + 26x^5 - 45x^4 - 25x^3 + 12x^2 + 5x - 1	\( 3^{4}\cdot 5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2} \)	16T1553	Trivial
16.8.7772051865600000000.1	x^16 - 4x^15 + 4x^14 + 12x^13 - 53x^12 + 72x^11 - 174x^9 + 253x^8 - 62x^7 - 226x^6 + 274x^5 - 57x^4 - 90x^3 + 62x^2 - 14x + 1	\( 2^{24}\cdot 3^{4}\cdot 5^{8}\cdot 11^{4} \)	$C_2^4.C_2^4$ (as 16T573)	Trivial (GRH)
16.8.7970073583641015625.1	x^16 - 2x^15 - 9x^14 + 23x^13 + 18x^12 - 82x^11 + 7x^10 + 140x^9 - 64x^8 - 130x^7 + 78x^6 + 76x^5 - 37x^4 - 31x^3 + 4x^2 + 6x + 1	\( 5^{8}\cdot 29^{4}\cdot 41^{2}\cdot 131^{2} \)	16T1340	Trivial (GRH)
16.8.8294667542637416704.1	x^16 - x^14 - 11x^12 + 12x^10 + 25x^8 - 40x^6 + 18x^4 - 4x^2 + 1	\( 2^{8}\cdot 19^{4}\cdot 47^{2}\cdot 103^{4} \)	16T1852	Trivial
16.8.8310412719464453125.1	x^16 - x^15 - 7x^14 + 14x^13 + 15x^12 - 48x^11 + 3x^10 + 73x^9 - 28x^8 - 110x^7 + 88x^6 + 99x^5 - 187x^4 + 105x^3 - 12x^2 - 7x + 1	\( 5^{8}\cdot 11^{6}\cdot 229^{3} \)	16T1432	Trivial
16.8.8310412719464453125.2	x^16 - 5x^15 + 5x^14 + 13x^13 - 28x^12 + 2x^11 + 36x^10 - 27x^9 - 29x^8 + 27x^7 + 36x^6 - 2x^5 - 28x^4 - 13x^3 + 5x^2 + 5x + 1	\( 5^{8}\cdot 11^{6}\cdot 229^{3} \)	16T1741	Trivial (GRH)
16.8.8503056000000000000.1	x^16 - 8x^15 + 22x^14 - 14x^13 - 46x^12 + 94x^11 - 56x^10 + 38x^9 - 92x^8 + 30x^7 + 100x^6 - 60x^5 - 23x^4 + 4x^3 + 4x^2 + 6x + 1	\( 2^{16}\cdot 3^{12}\cdot 5^{12} \)	$C_4 \times D_4$ (as 16T19)	Trivial (GRH)
16.8.8564920714097025129.1	x^16 - x^15 + 5x^13 - 12x^12 - 4x^11 + 9x^10 - 24x^9 + 6x^8 + 40x^7 + 30x^6 + 20x^5 - 18x^4 - 26x^3 - x^2 + 5x + 1	\( 3^{8}\cdot 19^{4}\cdot 89\cdot 103^{4} \)	16T1879	Trivial
16.8.8795570003734765625.1	x^16 - 5x^15 + 2x^14 + 32x^13 - 58x^12 - 51x^11 + 221x^10 - 70x^9 - 337x^8 + 302x^7 + 183x^6 - 327x^5 + 40x^4 + 117x^3 - 53x^2 + 3x + 1	\( 5^{8}\cdot 11^{4}\cdot 19^{4}\cdot 11801 \)	16T1719	Trivial (GRH)
16.8.9005368310736355328.1	x^16 - 4x^15 + 2x^14 + 12x^13 - 21x^12 + 52x^10 - 116x^9 + 160x^8 - 140x^7 + 38x^6 + 100x^5 - 170x^4 + 108x^3 - 18x^2 - 4x + 1	\( 2^{24}\cdot 41^{6}\cdot 113 \)	16T1722	Trivial
16.8.9349208943630483456.1	x^16 - 4x^15 - 2x^14 + 20x^13 - 5x^12 - 36x^11 + 28x^10 + 20x^9 - 62x^8 + 12x^7 + 78x^6 - 8x^5 - 54x^4 - 12x^3 + 16x^2 + 8x + 1	\( 2^{44}\cdot 3^{12} \)	$C_4\times S_4$ (as 16T181)	Trivial
16.8.9680638207773828125.1	x^16 - 2x^15 - 3x^14 + 4x^13 + 15x^12 + 7x^11 - 59x^10 - 48x^9 + 99x^8 + 100x^7 - 63x^6 - 89x^5 + 3x^4 + 31x^3 + 7x^2 - 3x - 1	\( 5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2}\cdot 101 \)	16T1823	Trivial
16.8.9680638207773828125.2	x^16 - 4x^15 + 4x^14 + 6x^13 - 33x^12 + 38x^11 + 10x^10 - 84x^9 + 103x^8 + 14x^7 - 80x^6 + 22x^5 + 3x^4 - 7x^3 + 9x^2 - 1	\( 5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2}\cdot 101 \)	16T1823	Trivial
16.8.9834496000000000000.1	x^16 - 4x^15 + 14x^13 - 2x^12 - 18x^11 - 26x^10 + 18x^9 + 81x^8 - 14x^7 - 98x^6 - 2x^5 + 60x^4 + 6x^3 - 16x^2 + 1	\( 2^{24}\cdot 5^{12}\cdot 7^{4} \)	$C_4\times S_4$ (as 16T181)	Trivial
16.8.9852069363500390625.1	x^16 - x^15 - 5x^14 + 3x^13 + 6x^12 + 4x^11 - 3x^10 - 6x^9 + x^8 - 6x^7 - 3x^6 + 4x^5 + 6x^4 + 3x^3 - 5x^2 - x + 1	\( 3^{12}\cdot 5^{8}\cdot 83^{4} \)	$C_2^3:S_4.C_2$ (as 16T763)	Trivial (GRH)
16.8.10447421432151953125.1	x^16 - 2x^15 - 4x^14 + 10x^13 - x^12 + 2x^10 - 51x^9 + 37x^8 + 75x^7 - 59x^6 - 38x^5 + 25x^4 + x^3 - x^2 + 5x + 1	\( 5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2}\cdot 109 \)	16T1823	Trivial
16.8.10621340052971585536.1	x^16 - 10x^14 + 31x^12 - 32x^10 + 21x^8 - 32x^6 + 31x^4 - 10x^2 + 1	\( 2^{32}\cdot 223^{4} \)	$C_2\times C_2^3:S_4$ (as 16T747)	Trivial (GRH)
16.8.10813142705316560896.1	x^16 - 12x^14 + 58x^12 - 152x^10 + 215x^8 - 128x^6 + 14x^4 + 4x^2 + 1	\( 2^{52}\cdot 7^{4} \)	$C_2^5.C_2$ (as 16T79)	Trivial (GRH)
16.8.10918012907706908672.1	x^16 - 2x^15 - 3x^14 + 8x^13 - 6x^12 + 2x^11 + 4x^10 - 2x^9 + 32x^8 - 62x^7 + 23x^6 - 8x^5 + 8x^4 + 6x^3 - 3x^2 + 2x + 1	\( 2^{24}\cdot 41^{6}\cdot 137 \)	16T1722	Trivial
16.8.11007531417600000000.1	x^16 - 4x^15 + 2x^14 + 8x^13 - 19x^12 + 8x^11 - 4x^10 + 76x^9 + 48x^8 - 120x^7 + 8x^6 + 68x^5 - 8x^4 - 12x^3 - 4x^2 + 1	\( 2^{32}\cdot 3^{8}\cdot 5^{8} \)	$C_2 \times (C_4\times C_2):C_2$ (as 16T18)	Trivial (GRH)
16.8.11161211905600000000.1	x^16 - 6x^14 + x^12 + 25x^10 - 70x^8 + 75x^6 - 29x^4 + x^2 + 1	\( 2^{12}\cdot 5^{8}\cdot 17^{8} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.8.11291175054931640625.1	x^16 - 4x^15 + x^14 + 4x^13 + 8x^12 - 4x^11 - x^10 - 23x^9 + 13x^8 + 61x^7 - 139x^6 + 62x^5 + 53x^4 - 23x^3 - 11x^2 + 2x + 1	\( 3^{12}\cdot 5^{14}\cdot 59^{2} \)	$C_2^3.C_2^4.C_2$ (as 16T554)	Trivial
16.8.11383787432672265625.1	x^16 - 4x^15 + 3x^14 + x^13 - 14x^12 + 32x^11 + 15x^10 + x^9 + 51x^8 + x^7 + 15x^6 + 32x^5 - 14x^4 + x^3 + 3x^2 - 4x + 1	\( 5^{8}\cdot 7^{4}\cdot 29^{4}\cdot 131^{2} \)	16T1116	Trivial
16.8.11597596268719140625.1	x^16 - 3x^15 - 2x^14 + 5x^13 + 8x^12 + 7x^10 - 33x^9 - 43x^8 + 49x^7 + 73x^6 - 9x^5 - 109x^4 + 55x^3 + 10x^2 - 9x + 1	\( 5^{8}\cdot 11^{2}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2} \)	16T1340	Trivial
16.8.11597596268719140625.2	x^16 - 2x^15 - 6x^14 + 13x^13 + 7x^12 - 9x^11 + 7x^10 - 72x^9 + 2x^8 + 83x^7 - 15x^6 + 72x^5 - 58x^4 - 54x^3 + 41x^2 - 10x + 1	\( 5^{8}\cdot 11^{2}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2} \)	16T1340	Trivial
16.8.11960209947718200609.1	x^16 - 4x^15 - x^14 + 13x^13 + 2x^12 - 8x^11 - 13x^10 + x^9 + 27x^8 + x^7 - 13x^6 - 8x^5 + 2x^4 + 13x^3 - x^2 - 4x + 1	\( 3^{2}\cdot 7^{2}\cdot 19^{4}\cdot 43^{2}\cdot 103^{4} \)	16T1664	Trivial (GRH)