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 570)

Label	Polynomial	Discriminant	Galois group	Class group
18.14.1107081869040352851890176.1	x^18 - 16x^16 + 95x^14 - 253x^12 + 273x^10 - 10x^8 - 169x^6 + 89x^4 - 8x^2 - 1	\( 2^{12}\cdot 37^{4}\cdot 229^{6} \)	18T711	Trivial (GRH)
18.14.1256584347701942722269184.1	x^18 - 5x^16 - 13x^14 + 139x^12 - 363x^10 + 412x^8 - 183x^6 + x^4 + 11x^2 - 1	\( 2^{12}\cdot 7^{12}\cdot 53^{6} \)	18T269	Trivial (GRH)
18.14.1546494554874388003652089.1	x^18 - 2x^17 - 8x^16 + 21x^15 + 2x^14 - 62x^13 + 90x^12 + 20x^11 - 141x^10 + 98x^9 - 36x^8 - 104x^7 + 183x^6 + 32x^5 - 110x^4 - 2x^3 + 20x^2 - 1	\( 7^{12}\cdot 53^{6}\cdot 71^{2} \)	18T269	Trivial (GRH)
18.14.1821632477226108224536576.1	x^18 - 11x^16 + 40x^14 - 50x^12 - x^10 + 25x^8 + 23x^6 - 38x^4 + 13x^2 - 1	\( 2^{18}\cdot 2791^{2}\cdot 944497^{2} \)	18T964	Trivial (GRH)
18.14.2047104877383620556488704.1	x^18 - 9x^16 + 32x^14 - 74x^12 + 152x^10 - 221x^8 + 180x^6 - 76x^4 + 15x^2 - 1	\( 2^{18}\cdot 23^{2}\cdot 5569^{2}\cdot 21817^{2} \)	18T964	Trivial (GRH)
18.14.2886523956915912859821961.1	x^18 - 3x^17 - 15x^16 + 46x^15 + 74x^14 - 231x^13 - 192x^12 + 540x^11 + 331x^10 - 667x^9 - 403x^8 + 457x^7 + 333x^6 - 147x^5 - 160x^4 - 4x^3 + 30x^2 + 10x + 1	\( 7^{12}\cdot 53^{6}\cdot 97^{2} \)	18T463	Trivial (GRH)
18.14.2886523956915912859821961.2	x^18 - x^17 - 15x^16 + 4x^15 + 92x^14 + 35x^13 - 280x^12 - 255x^11 + 411x^10 + 603x^9 - 209x^8 - 649x^7 - 93x^6 + 331x^5 + 126x^4 - 70x^3 - 34x^2 + 3x + 1	\( 7^{12}\cdot 53^{6}\cdot 97^{2} \)	18T463	Trivial (GRH)
18.14.3079475991408027794037529.1	x^18 - 9x^17 + 24x^16 + 12x^15 - 151x^14 + 133x^13 + 328x^12 - 499x^11 - 350x^10 + 771x^9 + 235x^8 - 655x^7 - 141x^6 + 322x^5 + 67x^4 - 81x^3 - 14x^2 + 7x + 1	\( 41\cdot 641^{2}\cdot 1721\cdot 10306187^{2} \)	18T968	Trivial (GRH)
18.14.4627653845488381463962761.1	x^18 - 15x^16 - 15x^15 + 54x^14 + 114x^13 - 32x^12 - 327x^11 - 102x^10 + 457x^9 + 102x^8 - 327x^7 + 32x^6 + 114x^5 - 54x^4 - 15x^3 + 15x^2 - 1	\( 3^{24}\cdot 199^{2}\cdot 20341^{2} \)	18T703	Trivial (GRH)
18.14.5285331976352154880724992.1	x^18 - 3x^17 - 4x^16 + 9x^15 - 25x^14 + 11x^13 + 105x^12 + 58x^11 - 71x^10 - 273x^9 - 220x^8 + 252x^7 + 374x^6 + 3x^5 - 170x^4 - 64x^3 + 9x^2 + 8x + 1	\( 2^{12}\cdot 23^{2}\cdot 37^{9}\cdot 137^{2} \)	18T319	Trivial (GRH)
18.14.6576752670755330244294481.1	x^18 - 3x^17 - 14x^16 + 47x^15 + 79x^14 - 321x^13 - 234x^12 + 1356x^11 + 76x^10 - 3435x^9 + 1672x^8 + 4094x^7 - 3619x^6 - 1450x^5 + 2070x^4 - 70x^3 - 260x^2 + 11x + 1	\( 19^{16}\cdot 151^{2} \)	18T177	Trivial (GRH)
18.14.6661494592726175761825792.1	x^18 - 13x^16 - 6x^15 + 65x^14 + 40x^13 - 140x^12 - 98x^11 + 82x^10 + 120x^9 + 123x^8 - 78x^7 - 197x^6 + 24x^5 + 97x^4 - 2x^3 - 18x^2 + 1	\( 2^{18}\cdot 37^{7}\cdot 16361^{2} \)	18T884	Trivial (GRH)
18.14.6661494592726175761825792.2	x^18 - 2x^17 - 16x^16 + 34x^15 + 65x^14 - 104x^13 - 173x^12 + 22x^11 + 325x^10 + 354x^9 - 242x^8 - 556x^7 - 72x^6 + 254x^5 + 65x^4 - 64x^3 - 7x^2 + 8x - 1	\( 2^{18}\cdot 37^{7}\cdot 16361^{2} \)	18T884	Trivial (GRH)
18.14.6987344124373460037357568.1	x^18 - 4x^17 - 7x^16 + 30x^15 - 69x^13 + 86x^12 + 46x^11 - 202x^10 - 31x^9 + 157x^8 + 148x^7 - 29x^6 - 187x^5 - 3x^4 + 77x^3 - 4x^2 - 9x + 1	\( 2^{12}\cdot 37^{9}\cdot 3623^{2} \)	18T319	Trivial (GRH)
18.14.10145719923049728269615104.1	x^18 - 12x^16 + 54x^14 - 117x^12 + 134x^10 - 99x^8 + 73x^6 - 44x^4 + 12x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 52879^{2} \)	18T703	Trivial (GRH)
18.14.11522585241472304020455424.1	x^18 - 10x^16 + 29x^14 - 7x^12 - 77x^10 + 72x^8 + 26x^6 - 45x^4 + 13x^2 - 1	\( 2^{24}\cdot 37^{6}\cdot 16361^{2} \)	18T883	Trivial (GRH)
18.14.11522585241472304020455424.2	x^18 - 8x^16 + 13x^14 + 29x^12 - 85x^10 + 30x^8 + 58x^6 - 51x^4 + 13x^2 - 1	\( 2^{24}\cdot 37^{6}\cdot 16361^{2} \)	18T883	Trivial (GRH)
18.14.11522585241472304020455424.3	x^18 - 4x^16 - 21x^14 + 81x^12 + 51x^10 - 374x^8 + 400x^6 - 155x^4 + 23x^2 - 1	\( 2^{24}\cdot 37^{6}\cdot 16361^{2} \)	18T776	Trivial (GRH)
18.14.12628145788322551940386816.1	x^18 - 5x^17 - 6x^16 + 62x^15 - 49x^14 - 199x^13 + 362x^12 + 75x^11 - 652x^10 + 313x^9 + 492x^8 - 341x^7 - 252x^6 + 157x^5 + 89x^4 - 36x^3 - 16x^2 + 3x + 1	\( 2^{12}\cdot 37^{6}\cdot 67^{2}\cdot 16361^{2} \)	18T776	Trivial (GRH)
18.14.13572219589547129158203125.1	x^18 - 2x^17 - 10x^16 + 8x^15 + 29x^14 + 46x^13 + 23x^12 - 231x^11 - 237x^10 + 224x^9 + 201x^8 - 78x^7 + 19x^6 + 17x^5 - 64x^4 - 4x^3 + 18x^2 - 1	\( 5^{9}\cdot 2791^{2}\cdot 944497^{2} \)	18T913	Trivial (GRH)
18.14.14610422921440715006545693.1	x^18 - 5x^17 - 2x^16 + 33x^15 + 15x^14 - 104x^13 - 297x^12 + 691x^11 + 676x^10 - 2335x^9 + 1040x^8 + 1412x^7 - 1939x^6 + 962x^5 + 320x^4 - 738x^3 + 262x^2 + 8x - 1	\( 19^{16}\cdot 37^{3} \)	18T460	Trivial (GRH)
18.14.16012035393449278995173376.1	x^18 - 15x^16 + 84x^14 - 206x^12 + 141x^10 + 291x^8 - 545x^6 + 219x^4 + 39x^2 - 1	\( 2^{12}\cdot 3^{24}\cdot 7^{12} \)	18T178	Trivial (GRH)
18.14.23938732941063497418391621.1	x^18 - 9x^17 + 23x^16 + 20x^15 - 173x^14 + 147x^13 + 383x^12 - 647x^11 - 244x^10 + 978x^9 - 198x^8 - 649x^7 + 330x^6 + 166x^5 - 143x^4 - 4x^3 + 21x^2 - 2x - 1	\( 7^{12}\cdot 13\cdot 41\cdot 113\cdot 169457^{2} \)	18T879	Trivial (GRH)
18.14.24593947462164109131513856.1	x^18 - 11x^16 + 45x^14 - 80x^12 + 40x^10 + 54x^8 - 69x^6 + 17x^4 + 3x^2 - 1	\( 2^{18}\cdot 9685993193^{2} \)	18T964	Trivial (GRH)
18.14.25060147842334579130105856.1	x^18 - 15x^16 + 105x^14 - 437x^12 + 1129x^10 - 1753x^8 + 1488x^6 - 554x^4 + 45x^2 - 1	\( 2^{30}\cdot 3^{4}\cdot 257^{6} \)	18T483	Trivial (GRH)
18.14.36374607805480156224815104.1	x^18 - 9x^16 + 27x^14 - 23x^12 - 29x^10 + 54x^8 - 8x^6 - 20x^4 + 9x^2 - 1	\( 2^{18}\cdot 11779563529^{2} \)	18T964	Trivial (GRH)
18.14.40962029154493055519936512.1	x^18 - 3x^17 - 7x^16 + 41x^15 - 41x^14 - 183x^13 + 425x^12 + 180x^11 - 989x^10 + 557x^9 + 389x^8 - 1221x^7 + 568x^6 + 1110x^5 - 312x^4 - 475x^3 - 95x^2 + x + 1	\( 2^{12}\cdot 37^{5}\cdot 229^{6} \)	18T764	Trivial (GRH)
18.14.40962029154493055519936512.2	x^18 - 14x^16 + 46x^14 + 104x^12 - 753x^10 + 947x^8 + 336x^6 - 1221x^4 + 592x^2 - 37	\( 2^{12}\cdot 37^{5}\cdot 229^{6} \)	18T764	Trivial (GRH)
18.14.47083412179823272799240192.1	x^18 - 14x^16 + 56x^14 - 36x^12 - 175x^10 + 144x^8 + 462x^6 - 738x^4 + 322x^2 - 23	\( 2^{18}\cdot 23^{3}\cdot 5569^{2}\cdot 21817^{2} \)	18T968	Trivial (GRH)
18.14.65162373998603777427181329.1	x^18 - 3x^17 - 9x^16 + 42x^15 - 9x^14 - 174x^13 + 244x^12 + 207x^11 - 702x^10 + 152x^9 + 813x^8 - 489x^7 - 397x^6 + 342x^5 + 54x^4 - 84x^3 + 6x^2 + 6x - 1	\( 3^{24}\cdot 15189497^{2} \)	18T703	Trivial (GRH)
18.14.69140512696962724890148864.1	x^18 - 9x^16 + 25x^14 - 11x^12 - 50x^10 + 57x^8 + 13x^6 - 36x^4 + 12x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 138041^{2} \)	18T838	Trivial (GRH)
18.14.70853239618582582520971264.1	x^18 - 12x^16 + 47x^14 - 59x^12 - 53x^10 + 198x^8 - 168x^6 + 49x^4 - x^2 - 1	\( 2^{18}\cdot 37^{4}\cdot 229^{6} \)	18T566	Trivial (GRH)
18.14.70853239618582582520971264.2	x^18 - 5x^16 - 7x^14 + 65x^12 - 76x^10 - 37x^8 + 105x^6 - 59x^4 + 13x^2 - 1	\( 2^{18}\cdot 37^{4}\cdot 229^{6} \)	18T566	Trivial (GRH)
18.14.70853239618582582520971264.3	x^18 - 13x^16 + 47x^14 - 30x^12 - 95x^10 + 120x^8 + 25x^6 - 76x^4 + 23x^2 - 1	\( 2^{18}\cdot 37^{4}\cdot 229^{6} \)	18T711	Trivial (GRH)
18.14.70853239618582582520971264.4	x^18 - 6x^16 + 5x^14 + 35x^12 - 88x^10 + 52x^8 + 36x^6 - 46x^4 + 13x^2 - 1	\( 2^{18}\cdot 37^{4}\cdot 229^{6} \)	18T711	Trivial (GRH)
18.14.70853239618582582520971264.5	x^18 - 11x^16 + 34x^14 + 16x^12 - 255x^10 + 452x^8 - 290x^6 + 35x^4 + 18x^2 - 1	\( 2^{18}\cdot 37^{4}\cdot 229^{6} \)	18T711	Trivial (GRH)
18.14.71020039461348097887305728.1	x^18 - 12x^16 + 70x^14 - 261x^12 + 637x^10 - 972x^8 + 874x^6 - 427x^4 + 98x^2 - 7	\( 2^{18}\cdot 7^{13}\cdot 52879^{2} \)	18T768	Trivial (GRH)
18.14.71020039461348097887305728.2	x^18 - 3x^16 - 33x^14 + 120x^12 + 193x^10 - 1167x^8 + 1499x^6 - 728x^4 + 126x^2 - 7	\( 2^{18}\cdot 7^{13}\cdot 52879^{2} \)	18T768	Trivial (GRH)
18.14.75591504000497820001953125.1	x^18 - 2x^17 - 19x^16 + 38x^15 + 118x^14 - 245x^13 - 329x^12 + 701x^11 + 606x^10 - 970x^9 - 800x^8 + 626x^7 + 622x^6 - 136x^5 - 224x^4 - 14x^3 + 25x^2 + 2x - 1	\( 5^{9}\cdot 7^{12}\cdot 52879^{2} \)	18T286	Trivial (GRH)
18.14.75613185918270483380568064.1	x^18 - 7x^16 + 7x^14 + 45x^12 - 100x^10 - 13x^8 + 170x^6 - 139x^4 + 36x^2 - 1	\( 2^{18}\cdot 19^{16} \)	18T177	Trivial (GRH)
18.14.75613185918270483380568064.2	x^18 - 9x^16 + 17x^14 + 49x^12 - 178x^10 + 83x^8 + 160x^6 - 131x^4 + 28x^2 - 1	\( 2^{18}\cdot 19^{16} \)	18T368	Trivial (GRH)
18.14.75613185918270483380568064.3	x^18 - 7x^16 + 7x^14 + 45x^12 - 119x^10 + 63x^8 + 75x^6 - 82x^4 + 17x^2 - 1	\( 2^{18}\cdot 19^{16} \)	18T368	Trivial (GRH)
18.14.80421398252924334225227776.1	x^18 - 10x^16 + 32x^14 - 20x^12 - 86x^10 + 172x^8 - 101x^6 + 6x^4 + 8x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 53^{6} \)	18T268	Trivial (GRH)
18.14.80421398252924334225227776.2	x^18 - 7x^16 + 3x^14 + 46x^12 - 67x^10 - 41x^8 + 130x^6 - 80x^4 + 17x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 53^{6} \)	18T268	Trivial (GRH)
18.14.80421398252924334225227776.3	x^18 - x^16 - 22x^14 + 62x^12 - 8x^10 - 144x^8 + 185x^6 - 91x^4 + 18x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 53^{6} \)	18T463	Trivial (GRH)
18.14.80421398252924334225227776.4	x^18 - 13x^16 + 65x^14 - 146x^12 + 87x^10 + 240x^8 - 507x^6 + 362x^4 - 87x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 53^{6} \)	18T463	Trivial (GRH)
18.14.81542670543816541216178176.1	x^18 - 16x^16 + 92x^14 - 217x^12 + 112x^10 + 273x^8 - 232x^6 - 103x^4 + 27x^2 - 1	\( 2^{18}\cdot 19^{6}\cdot 137^{6} \)	18T630	Trivial (GRH)
18.14.88133009763711378710013049.1	x^18 - 9x^17 + 24x^16 + 12x^15 - 158x^14 + 182x^13 + 237x^12 - 590x^11 + 78x^10 + 633x^9 - 417x^8 - 222x^7 + 311x^6 - 26x^5 - 86x^4 + 24x^3 + 10x^2 - 4x - 1	\( 7^{12}\cdot 53^{6}\cdot 287281 \)	18T544	Trivial (GRH)
18.14.104192253035948620552339456.1	x^18 - 7x^16 + x^14 + 85x^12 - 226x^10 + 220x^8 - 66x^6 - 17x^4 + 11x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 169457^{2} \)	18T703	Trivial (GRH)
18.14.104192253035948620552339456.2	x^18 - 4x^16 - 16x^14 + 69x^12 + 3x^10 - 232x^8 + 290x^6 - 133x^4 + 22x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 169457^{2} \)	18T838	Trivial (GRH)