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 112)

Label	Polynomial	Discriminant	Galois group	Class group
18.2.7182890828838813137.1	x^18 - 5x^17 + 12x^16 - 22x^15 + 39x^14 - 63x^13 + 85x^12 - 97x^11 + 99x^10 - 98x^9 + 91x^8 - 71x^7 + 53x^6 - 44x^5 + 29x^4 - 15x^3 + 10x^2 - 4x + 1	\( 7^{12}\cdot 113\cdot 2143^{2} \)	18T879	Trivial
18.0.122528889346354745723.1	x^18 - 9x^17 + 43x^16 - 140x^15 + 345x^14 - 679x^13 + 1105x^12 - 1521x^11 + 1799x^10 - 1845x^9 + 1649x^8 - 1285x^7 + 872x^6 - 512x^5 + 256x^4 - 105x^3 + 34x^2 - 8x + 1	\( -\,7^{12}\cdot 1399^{2}\cdot 4523 \)	18T879	Trivial
18.4.1005745241518950615011.1	x^18 - 3x^17 + x^16 + 8x^15 - 10x^14 - 3x^13 + 15x^12 - 8x^11 + 5x^10 - 14x^9 - 6x^8 + 62x^7 - 84x^6 + 28x^5 + 44x^4 - 60x^3 + 33x^2 - 9x + 1	\( -\,7^{12}\cdot 1091\cdot 8161^{2} \)	18T879	Trivial
18.6.6604176220601368377521.1	x^18 - 5x^17 + 10x^16 - 14x^15 + 19x^14 - 13x^13 - 19x^12 + 80x^11 - 163x^10 + 226x^9 - 229x^8 + 132x^7 + 26x^6 - 139x^5 + 181x^4 - 133x^3 + 49x^2 + 19x - 29	\( 7^{12}\cdot 41\cdot 1931^{2}\cdot 3121 \)	18T879	Trivial
18.4.7101528447669869215744.3	x^18 + x^16 - 6x^14 + 4x^12 + 3x^10 + 5x^8 - 8x^6 + 4x^4 - 4x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 1399^{2} \)	18T879	Trivial
18.4.7101528447669869215744.4	x^18 - 7x^16 + 20x^14 - 32x^12 + 33x^10 - 23x^8 + 11x^6 - 2x^4 - x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 1399^{2} \)	18T879	Trivial
18.4.16927637793612848674267.1	x^18 - 9x^17 + 43x^16 - 140x^15 + 343x^14 - 665x^13 + 1052x^12 - 1385x^11 + 1537x^10 - 1448x^9 + 1157x^8 - 775x^7 + 421x^6 - 172x^5 + 39x^4 + 8x^3 - 14x^2 + 7x - 1	\( -\,7^{12}\cdot 41^{2}\cdot 97^{2}\cdot 77323 \)	18T879	Trivial
18.2.24724476901703653513873.3	x^18 - 4x^17 + 11x^16 - 18x^15 + 29x^14 - 63x^13 + 93x^12 - 137x^11 + 172x^10 - 143x^9 + 196x^8 - 138x^7 - 32x^6 + 24x^5 - 169x^4 + 250x^3 - 155x^2 + 223x - 139	\( 7^{12}\cdot 97^{3}\cdot 1399^{2} \)	18T879	Trivial
18.6.35696621131010569510753.1	x^18 - x^17 - 8x^16 + 13x^15 + 34x^14 - 54x^13 - 96x^12 + 103x^11 + 163x^10 - 103x^9 - 169x^8 + 21x^7 + 155x^6 + 161x^5 - 93x^4 - 292x^3 - 30x^2 + 153x + 43	\( 7^{12}\cdot 41^{4}\cdot 97^{3} \)	18T879	Trivial
18.2.35696621131010569510753.1	x^18 - 6x^17 + 25x^16 - 75x^15 + 165x^14 - 293x^13 + 390x^12 - 434x^11 + 403x^10 - 393x^9 + 403x^8 - 434x^7 + 390x^6 - 293x^5 + 165x^4 - 75x^3 + 25x^2 - 6x + 1	\( 7^{12}\cdot 41^{4}\cdot 97^{3} \)	18T879	Trivial
18.6.35696621131010569510753.2	x^18 - x^17 - 5x^16 + 4x^15 + x^14 - 3x^13 + 49x^12 + 41x^11 - 101x^10 - 151x^9 + 13x^8 + 140x^7 + 91x^6 - 11x^5 - 40x^4 - 5x^3 + 5x^2 - 1	\( 7^{12}\cdot 41^{4}\cdot 97^{3} \)	18T879	Trivial
18.6.36578872938484796669433.2	x^18 - 3x^17 + 6x^15 - 9x^14 + 12x^13 - 7x^12 + 3x^11 - 3x^10 + x^9 - 3x^8 + 3x^7 - 7x^6 + 12x^5 - 9x^4 + 6x^3 - 3x + 1	\( 3^{24}\cdot 73^{3}\cdot 577^{2} \)	18T879	Trivial
18.6.36578872938484796669433.3	x^18 - 3x^16 - 6x^15 - 9x^14 - 6x^13 + 2x^12 + 15x^11 + 27x^10 + 31x^9 + 27x^8 + 15x^7 + 2x^6 - 6x^5 - 9x^4 - 6x^3 - 3x^2 + 1	\( 3^{24}\cdot 73^{3}\cdot 577^{2} \)	18T879	Trivial
18.8.57388858189268996325376.1	x^18 - 10x^16 + 39x^14 - 75x^12 + 66x^10 + x^8 - 52x^6 + 42x^4 - 12x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2} \)	18T879	Trivial (GRH)
18.8.57388858189268996325376.2	x^18 - 6x^16 + 16x^14 - 12x^12 - 15x^10 + 4x^8 + 18x^6 - 6x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2} \)	18T879	Trivial (GRH)
18.4.57388858189268996325376.2	x^18 + 2x^16 - 2x^14 + 6x^12 - 10x^10 - 19x^8 + 36x^6 - 3x^4 - 11x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2} \)	18T879	Trivial
18.4.57388858189268996325376.3	x^18 + 7x^16 + 22x^14 + 41x^12 + 47x^10 + 25x^8 - 10x^6 - 18x^4 - 3x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2} \)	18T879	Trivial
18.8.57388858189268996325376.3	x^18 - 3x^14 - x^12 - 4x^10 + 2x^8 + 11x^6 - x^4 - 5x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2} \)	18T879	Trivial (GRH)
18.8.57388858189268996325376.4	x^18 - 9x^16 + 34x^14 - 73x^12 + 101x^10 - 106x^8 + 73x^6 - 23x^4 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2} \)	18T879	Trivial (GRH)
18.6.84452981700195737623001.1	x^18 - 6x^17 + 16x^16 - 33x^15 + 55x^14 - 93x^13 + 206x^12 - 458x^11 + 922x^10 - 1413x^9 + 1639x^8 - 1472x^7 + 1057x^6 - 667x^5 + 432x^4 - 353x^3 + 166x^2 - 27x + 1	\( 7^{12}\cdot 41^{3}\cdot 97^{4} \)	18T879	Trivial (GRH)
18.10.148166223769011413199501.1	x^18 - 9x^17 + 27x^16 - 12x^15 - 93x^14 + 147x^13 + 83x^12 - 303x^11 + 24x^10 + 298x^9 - 69x^8 - 165x^7 + 18x^6 + 48x^5 + 21x^4 - 4x^3 - 12x^2 + 1	\( 3^{24}\cdot 19\cdot 2053^{2}\cdot 6551 \)	18T879	Trivial (GRH)
18.6.171417916195550289266477.1	x^18 - 3x^17 - x^16 + 8x^15 - 7x^14 + 20x^13 - 42x^12 - 36x^11 + 201x^10 + 86x^9 + 40x^8 - 688x^7 - 1362x^6 + 230x^5 + 1531x^4 + 1854x^3 + 1341x^2 + 257x - 71	\( 7^{12}\cdot 1399^{3}\cdot 4523 \)	18T879	Trivial (GRH)
18.2.199803395729731379254417.1	x^18 - x^17 + x^16 - 16x^15 + 3x^14 - 13x^13 + 80x^12 + 35x^11 + 89x^10 - 116x^9 - 186x^8 - 226x^7 + 20x^6 + 16x^5 - 544x^4 - 1212x^3 - 499x^2 + 48x + 181	\( 7^{12}\cdot 41^{2}\cdot 97^{5} \)	18T879	Trivial
18.10.289123420349393529839217.1	x^18 - 3x^17 + 12x^15 - 15x^14 - 15x^13 + 21x^12 + 33x^11 - 18x^10 - 114x^9 + 90x^8 + 171x^7 - 109x^6 - 105x^5 + 15x^4 + 24x^3 + 15x^2 - 3x - 1	\( 3^{24}\cdot 73^{2}\cdot 577^{3} \)	18T879	Trivial
18.10.289123420349393529839217.2	x^18 - 6x^16 - 3x^15 + 9x^14 + 21x^13 - x^12 - 21x^11 + 27x^10 - 60x^9 - 162x^8 - 3x^7 + 183x^6 + 162x^5 - 48x^4 - 92x^3 + 12x^2 + 9x - 1	\( 3^{24}\cdot 73^{2}\cdot 577^{3} \)	18T879	Trivial
18.10.289123420349393529839217.3	x^18 - 3x^17 - 9x^16 + 26x^15 + 18x^14 - 57x^13 + 9x^12 - 75x^10 + 123x^9 + 105x^8 - 129x^7 - 34x^6 + 51x^5 - 33x^4 - 20x^3 + 18x^2 + 9x + 1	\( 3^{24}\cdot 73^{2}\cdot 577^{3} \)	18T879	Trivial
18.10.289123420349393529839217.4	x^18 - 3x^17 + 20x^15 - 30x^14 - 66x^13 + 79x^12 + 147x^11 + 3x^10 - 107x^9 - 180x^8 - 210x^7 + 12x^6 + 273x^5 + 231x^4 + 48x^3 - 24x^2 - 12x - 1	\( 3^{24}\cdot 73^{2}\cdot 577^{3} \)	18T879	Trivial
18.4.298632708486259154687519.2	x^18 - 2x^16 - 8x^15 - 10x^14 + 32x^13 - 7x^12 + 86x^11 - 88x^10 + 38x^9 - 120x^8 - 30x^7 - 57x^6 + 68x^5 + 90x^4 + 82x^3 + 39x^2 + 12x + 1	\( -\,7^{15}\cdot 41^{3}\cdot 97^{3} \)	18T879	Trivial (GRH)
18.4.298632708486259154687519.3	x^18 - 6x^17 + 16x^16 - 27x^15 + 36x^14 - 23x^13 + 11x^12 - 106x^11 + 84x^10 + 187x^9 - 168x^8 - 128x^7 + 51x^6 + 266x^5 - 177x^4 - 230x^3 + 244x^2 + 53x - 83	\( -\,7^{15}\cdot 41^{3}\cdot 97^{3} \)	18T879	Trivial (GRH)
18.8.464557916992990226137543.1	x^18 - 9x^17 + 42x^16 - 132x^15 + 302x^14 - 518x^13 + 655x^12 - 550x^11 + 146x^10 + 403x^9 - 794x^8 + 818x^7 - 516x^6 + 139x^5 + 85x^4 - 117x^3 + 58x^2 - 13x + 1	\( -\,7^{12}\cdot 71\cdot 113\cdot 64679^{2} \)	18T879	Trivial
18.12.987629569339089510074691.2	x^18 - 6x^17 + 3x^16 + 41x^15 - 48x^14 - 153x^13 + 249x^12 + 276x^11 - 624x^10 - 165x^9 + 774x^8 - 90x^7 - 472x^6 + 132x^5 + 135x^4 - 38x^3 - 18x^2 + 3x + 1	\( -\,3^{27}\cdot 73^{3}\cdot 577^{2} \)	18T879	Trivial
18.12.987629569339089510074691.3	x^18 - 6x^16 - 4x^15 - 6x^14 + 51x^13 + 105x^12 - 186x^11 - 318x^10 + 237x^9 + 552x^8 + 18x^7 - 613x^6 - 237x^5 + 384x^4 + 112x^3 - 99x^2 + 9x + 1	\( -\,3^{27}\cdot 73^{3}\cdot 577^{2} \)	18T879	Trivial
18.12.2095795683329361973048159.1	x^18 - 2x^17 - 6x^16 + 14x^15 - 3x^14 - 32x^13 + 34x^12 + 19x^11 - 10x^10 - 51x^9 + 15x^8 + 90x^7 - 57x^6 - 57x^5 + 44x^4 + 14x^3 - 12x^2 - x + 1	\( -\,7^{12}\cdot 4591\cdot 181607^{2} \)	18T879	Trivial (GRH)
18.0.2352943185760028849340416.2	x^18 + 8x^16 + 26x^14 + 59x^12 + 145x^10 + 429x^8 + 780x^6 + 701x^4 + 287x^2 + 41	\( -\,2^{18}\cdot 7^{12}\cdot 41^{3}\cdot 97^{2} \)	18T879	Trivial
18.0.2352943185760028849340416.3	x^18 - 14x^14 + 8x^12 + 56x^10 - 49x^8 - 100x^6 + 84x^4 + 140x^2 + 41	\( -\,2^{18}\cdot 7^{12}\cdot 41^{3}\cdot 97^{2} \)	18T879	Trivial
18.6.2352943185760028849340416.1	x^18 - 2x^16 - 3x^14 + 11x^12 - 77x^10 + 95x^8 + 139x^6 - 232x^4 + 192x^2 - 41	\( 2^{18}\cdot 7^{12}\cdot 41^{3}\cdot 97^{2} \)	18T879	Trivial (GRH)
18.2.2352943185760028849340416.1	x^18 - 3x^16 - 18x^14 + 60x^12 + 60x^10 - 254x^8 - 22x^6 + 288x^4 - 41	\( 2^{18}\cdot 7^{12}\cdot 41^{3}\cdot 97^{2} \)	18T879	Trivial
18.2.2352943185760028849340416.2	x^18 + 9x^16 + 33x^14 + 83x^12 + 179x^10 + 310x^8 + 344x^6 + 32x^4 - 123x^2 - 41	\( 2^{18}\cdot 7^{12}\cdot 41^{3}\cdot 97^{2} \)	18T879	Trivial
18.10.2352943185760028849340416.2	x^18 - 17x^16 + 114x^14 - 381x^12 + 663x^10 - 599x^8 + 370x^6 - 320x^4 + 181x^2 - 41	\( 2^{18}\cdot 7^{12}\cdot 41^{3}\cdot 97^{2} \)	18T879	Trivial (GRH)
18.6.2352943185760028849340416.2	x^18 - 3x^16 - 3x^14 + 9x^12 + 3x^10 + 50x^8 - 108x^6 - 84x^4 + 205x^2 - 41	\( 2^{18}\cdot 7^{12}\cdot 41^{3}\cdot 97^{2} \)	18T879	Trivial (GRH)
18.6.2352943185760028849340416.3	x^18 - x^16 - 12x^14 - 29x^12 - 11x^10 + 159x^8 - 213x^6 + 51x^4 + 123x^2 - 41	\( 2^{18}\cdot 7^{12}\cdot 41^{3}\cdot 97^{2} \)	18T879	Trivial (GRH)
18.6.6497398218116128597530193.3	x^18 - x^17 - 4x^16 + 7x^15 - 31x^14 - 36x^13 + 95x^12 + 66x^11 + 240x^10 + 331x^9 - 76x^8 + 495x^7 - 45x^6 + 26x^5 + 513x^4 - 849x^3 + 940x^2 - 522x + 97	\( 7^{12}\cdot 97^{3}\cdot 22679^{2} \)	18T879	Trivial
18.6.6497398218116128597530193.4	x^18 - 3x^16 - 10x^15 - 40x^14 + 2x^13 - 54x^12 - 140x^11 - 176x^10 - 383x^9 + 14x^8 + 139x^7 + 712x^6 + 686x^5 + 654x^4 + 337x^3 + 129x^2 + 20x + 1	\( 7^{12}\cdot 97^{3}\cdot 22679^{2} \)	18T879	Trivial
18.8.7806332349433625305658859.1	x^18 - 3x^17 - 8x^15 + 21x^14 + 22x^12 + 12x^11 - 213x^10 + 401x^9 - 195x^8 + 330x^7 - 431x^6 - 1530x^5 + 1161x^4 + 1155x^3 - 69x^2 - 420x - 233	\( -\,3^{27}\cdot 73^{2}\cdot 577^{3} \)	18T879	Trivial
18.8.7806332349433625305658859.2	x^18 - 6x^17 + 6x^16 + 18x^15 - 51x^14 + 78x^13 - 27x^12 - 87x^11 + 222x^10 - 281x^9 + 222x^8 - 87x^7 - 27x^6 + 78x^5 - 51x^4 + 18x^3 + 6x^2 - 6x + 1	\( -\,3^{27}\cdot 73^{2}\cdot 577^{3} \)	18T879	Trivial
18.8.7806332349433625305658859.3	x^18 - 6x^17 + 18x^16 - 37x^15 + 21x^14 + 105x^13 - 324x^12 + 360x^11 + 162x^10 - 741x^9 + 651x^8 - 135x^7 - 367x^6 + 321x^5 - 93x^4 + 73x^3 - 60x^2 - 3x + 1	\( -\,3^{27}\cdot 73^{2}\cdot 577^{3} \)	18T879	Trivial
18.8.7806332349433625305658859.4	x^18 - 6x^16 - 10x^15 + 21x^13 + 40x^12 + 9x^11 - 60x^10 - 23x^9 - 27x^8 + 27x^7 - 2x^6 - 54x^5 + 90x^4 + 33x^3 - 36x^2 - 3x + 1	\( -\,3^{27}\cdot 73^{2}\cdot 577^{3} \)	18T879	Trivial
18.4.10145719923049728269615104.1	x^18 + 2x^16 - 11x^14 - 51x^12 - 90x^10 - 68x^8 + 5x^6 + 33x^4 + 11x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{2} \)	18T879	Trivial
18.4.10145719923049728269615104.2	x^18 + 2x^16 - x^14 - 2x^12 - 13x^10 - 16x^8 + 5x^6 + 15x^4 + 7x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{2} \)	18T879	Trivial (GRH)
18.12.10145719923049728269615104.2	x^18 - 8x^16 + 17x^14 + 12x^12 - 87x^10 + 121x^8 - 88x^6 + 43x^4 - 11x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{2} \)	18T879	Trivial (GRH)