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 all 47 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.25672039088801296000000000000.1	x^20 + 8x^18 + 28x^16 + 72x^14 + 141x^12 + 203x^10 + 230x^8 + 181x^6 + 80x^4 + 16x^2 + 1	\( 2^{16}\cdot 5^{12}\cdot 6329^{4} \)	20T1025	Trivial (GRH)
20.4.25672039088801296000000000000.3	x^20 - 6x^18 + 11x^16 - 2x^14 - 36x^12 + 52x^10 - 15x^8 - 102x^6 - 4x^4 + 20x^2 + 1	\( 2^{16}\cdot 5^{12}\cdot 6329^{4} \)	20T1025	Trivial (GRH)
20.8.25672039088801296000000000000.3	x^20 + 5x^18 + x^16 - 23x^14 - 20x^12 + 43x^10 + 24x^8 - 23x^6 - 9x^4 + x^2 + 1	\( 2^{16}\cdot 5^{12}\cdot 6329^{4} \)	20T1025	Trivial (GRH)
20.4.25672039088801296000000000000.4	x^20 + 3x^18 + 8x^16 - 8x^14 - 74x^12 + 33x^10 + 180x^8 - 44x^6 - 150x^4 - 14x^2 + 1	\( 2^{16}\cdot 5^{12}\cdot 6329^{4} \)	20T1025	Trivial (GRH)
20.8.25672039088801296000000000000.4	x^20 - 13x^18 + 64x^16 - 151x^14 + 198x^12 - 212x^10 + 166x^8 + 85x^6 - 152x^4 - 51x^2 + 1	\( 2^{16}\cdot 5^{12}\cdot 6329^{4} \)	20T1025	Trivial (GRH)
20.0.97531030166573056000000000000.2	x^20 + 5x^18 + 18x^16 + 79x^14 + 291x^12 + 348x^10 - 341x^8 - 437x^6 + 334x^4 + 625x^2 + 121	\( 2^{24}\cdot 5^{12}\cdot 47^{8} \)	20T1025	Trivial (GRH)
20.0.97531030166573056000000000000.3	x^20 - 7x^19 + 29x^18 - 97x^17 + 266x^16 - 615x^15 + 1280x^14 - 2427x^13 + 4197x^12 - 6412x^11 + 8704x^10 - 10813x^9 + 12227x^8 - 11913x^7 + 9115x^6 - 4910x^5 + 1756x^4 - 423x^3 + 74x^2 - 8x + 1	\( 2^{24}\cdot 5^{12}\cdot 47^{8} \)	20T1025	Trivial (GRH)
20.0.410752625420820736000000000000.2	x^20 + 12x^18 + 52x^16 + 93x^14 + 76x^12 + 226x^10 + 671x^8 + 530x^6 - 165x^4 - 100x^2 + 25	\( 2^{20}\cdot 5^{12}\cdot 6329^{4} \)	20T1025	Trivial (GRH)
20.4.426356047425299072265625000000.1	x^20 - 5x^19 + 10x^18 - 20x^17 + 5x^16 + 215x^15 - 890x^14 + 1915x^13 - 2520x^12 + 1775x^11 + 234x^10 - 1940x^9 + 1895x^8 - 620x^7 - 420x^6 + 630x^5 - 240x^4 - 125x^3 + 30x^2 - 5x - 1	\( 2^{6}\cdot 5^{20}\cdot 7^{8}\cdot 59^{4} \)	20T1025	Trivial (GRH)
20.8.690223904276486455197870063616.1	x^20 - 4x^19 + 4x^18 - 8x^17 + 27x^16 - 48x^15 + 94x^14 - 116x^13 + 162x^12 - 208x^11 + 288x^10 - 992x^9 - 380x^8 + 2816x^7 + 152x^6 - 2480x^5 - 232x^4 + 1088x^3 - 192x + 32	\( 2^{48}\cdot 31^{4}\cdot 227^{4} \)	20T1025	Trivial (GRH)
20.12.690223904276486455197870063616.3	x^20 - 58x^16 - 12x^14 + 361x^12 - 76x^10 - 604x^8 + 360x^6 + 144x^4 - 128x^2 + 16	\( 2^{48}\cdot 31^{4}\cdot 227^{4} \)	20T1025	Trivial (GRH)
20.12.1643010501683282944000000000000.1	x^20 + x^18 - 3x^16 - 42x^14 + 42x^12 + 79x^10 + 113x^8 - 473x^6 + 351x^4 - 78x^2 + 4	\( 2^{22}\cdot 5^{12}\cdot 6329^{4} \)	20T1025	Trivial (GRH)
20.4.1643010501683282944000000000000.1	x^20 + 8x^18 + 15x^16 - 35x^14 - 170x^12 - 187x^10 + 184x^8 + 710x^6 + 815x^4 + 450x^2 + 100	\( 2^{22}\cdot 5^{12}\cdot 6329^{4} \)	20T1025	Trivial (GRH)
20.12.1643010501683282944000000000000.2	x^20 - 16x^18 + 97x^16 - 252x^14 + 113x^12 + 693x^10 - 909x^8 - 691x^6 + 1395x^4 - 154x^2 + 4	\( 2^{22}\cdot 5^{12}\cdot 6329^{4} \)	20T1025	Trivial (GRH)
20.4.1938595627218483216000000000000.1	x^20 + 11x^18 + 45x^16 + 76x^14 + 25x^12 - 57x^10 - 49x^8 - 48x^6 - 57x^4 - 12x^2 + 1	\( 2^{16}\cdot 3^{12}\cdot 5^{12}\cdot 691^{4} \)	20T1025	Trivial (GRH)
20.8.2760895617105945820791480254464.1	x^20 + 6x^18 - 51x^16 - 100x^14 + 414x^12 + 544x^10 - 198x^8 - 364x^6 - 23x^4 + 42x^2 + 1	\( 2^{50}\cdot 31^{4}\cdot 227^{4} \)	20T1025	Trivial (GRH)
20.12.2760895617105945820791480254464.2	x^20 - 10x^18 - 35x^16 + 724x^14 - 2826x^12 + 3664x^10 - 454x^8 - 1252x^6 + 145x^4 + 106x^2 + 1	\( 2^{50}\cdot 31^{4}\cdot 227^{4} \)	20T1025	Trivial (GRH)
20.4.8909971276806250000000000000000.1	x^20 + 5x^18 + 25x^16 - 60x^14 - 490x^12 - 2094x^10 - 4080x^8 - 5215x^6 - 2415x^4 + 980x^2 + 784	\( 2^{16}\cdot 5^{20}\cdot 7^{6}\cdot 59^{4} \)	20T1025	Trivial (GRH)
20.4.11043582468423783283165921017856.1	x^20 + 14x^18 + 25x^16 - 452x^14 - 2814x^12 - 6312x^10 - 5426x^8 - 140x^6 + 1589x^4 + 330x^2 + 1	\( 2^{52}\cdot 31^{4}\cdot 227^{4} \)	20T1025	Trivial (GRH)
20.8.11043582468423783283165921017856.1	x^20 + 2x^18 - 4x^17 - 50x^16 - 8x^15 - 236x^14 - 344x^13 + 842x^12 - 272x^11 - 1668x^10 + 2472x^9 + 1736x^8 - 3456x^7 - 904x^6 + 2256x^5 + 208x^4 - 736x^3 + 96x - 8	\( 2^{52}\cdot 31^{4}\cdot 227^{4} \)	20T1025	Trivial (GRH)
20.4.15691000132788774317754150390625.1	x^20 - 5x^19 + 11x^18 - 60x^16 + 176x^15 + 151x^14 - 2140x^13 + 9120x^12 - 24090x^11 + 45830x^10 - 67547x^9 + 67541x^8 - 33683x^7 - 28555x^6 + 97314x^5 - 109879x^4 + 50637x^3 + 18615x^2 - 41617x + 18779	\( 5^{12}\cdot 6329^{6} \)	20T1025	Trivial (GRH)
20.0.124070120141982925824000000000000.1	x^20 + 5x^18 - 23x^16 - 82x^14 + 221x^12 + 194x^10 - 479x^8 + 121x^6 + 379x^4 + 90x^2 + 4	\( 2^{22}\cdot 3^{12}\cdot 5^{12}\cdot 691^{4} \)	20T1025	Trivial (GRH)
20.12.124070120141982925824000000000000.1	x^20 - 5x^18 - 23x^16 + 82x^14 + 221x^12 - 194x^10 - 479x^8 - 121x^6 + 379x^4 - 90x^2 + 4	\( 2^{22}\cdot 3^{12}\cdot 5^{12}\cdot 691^{4} \)	20T1025	Trivial (GRH)
20.4.124070120141982925824000000000000.1	x^20 - 2x^18 - 11x^16 + 14x^14 + 39x^12 - 31x^10 - 65x^8 + 9x^6 + 61x^4 + 30x^2 + 4	\( 2^{22}\cdot 3^{12}\cdot 5^{12}\cdot 691^{4} \)	20T1025	Trivial (GRH)
20.8.124070120141982925824000000000000.1	x^20 + 2x^18 - 11x^16 - 14x^14 + 39x^12 + 31x^10 - 65x^8 - 9x^6 + 61x^4 - 30x^2 + 4	\( 2^{22}\cdot 3^{12}\cdot 5^{12}\cdot 691^{4} \)	20T1025	Trivial (GRH)
20.8.279157770319461583104000000000000.1	x^20 - 12x^18 + 52x^16 - 90x^14 + 11x^12 + 141x^10 - 123x^8 - 3x^6 + 54x^4 - 36x^2 + 9	\( 2^{20}\cdot 3^{14}\cdot 5^{12}\cdot 691^{4} \)	20T1025	Trivial (GRH)
20.8.420610688430920433664000000000000.1	x^20 + 4x^18 - 56x^16 - 248x^14 + 480x^12 + 3296x^10 + 1664x^8 - 1024x^6 + 2048x^4 - 4608x^2 + 1024	\( 2^{30}\cdot 5^{12}\cdot 6329^{4} \)	20T1025	Trivial (GRH)
20.8.663305172009703483445153131134976.1	x^20 - 4x^19 - 12x^18 + 64x^17 - 47x^16 - 112x^15 + 52x^14 + 772x^13 + 819x^12 - 2776x^11 - 1954x^10 + 344x^9 + 9798x^8 - 4600x^7 - 3608x^6 - 6376x^5 + 12252x^4 - 2904x^3 - 3544x^2 + 2192x - 356	\( 2^{48}\cdot 31^{6}\cdot 227^{4} \)	20T1025	Trivial (GRH)
20.16.663305172009703483445153131134976.2	x^20 - 8x^19 + 20x^18 + 48x^17 - 425x^16 + 968x^15 - 50x^14 - 5468x^13 + 15723x^12 - 16620x^11 - 12984x^10 + 51256x^9 - 35780x^8 - 25088x^7 + 46526x^6 - 14064x^5 - 10940x^4 + 8860x^3 - 2128x^2 + 152x + 2	\( 2^{48}\cdot 31^{6}\cdot 227^{4} \)	20T1025	Trivial (GRH)
20.16.2653220688038813933780612524539904.1	x^20 - 4x^19 - 26x^18 + 152x^17 + 51x^16 - 1688x^15 + 2778x^14 + 5072x^13 - 22121x^12 + 18888x^11 + 39272x^10 - 118164x^9 + 95949x^8 + 92400x^7 - 279636x^6 + 225120x^5 + 7804x^4 - 136008x^3 + 92420x^2 - 24224x + 1966	\( 2^{50}\cdot 31^{6}\cdot 227^{4} \)	20T1025	Trivial (GRH)
20.4.2653220688038813933780612524539904.1	x^20 - 4x^19 - 6x^18 + 24x^17 + 57x^16 - 64x^15 - 634x^14 - 380x^13 + 2261x^12 + 4104x^11 - 11312x^10 - 21592x^9 + 19470x^8 + 61488x^7 + 5640x^6 - 37696x^5 + 70364x^4 - 1856x^3 + 15616x^2 + 18368x + 6712	\( 2^{50}\cdot 31^{6}\cdot 227^{4} \)	20T1025	$[2]$ (GRH)
20.0.7940487689086907252736000000000000.1	x^20 + 23x^18 + 277x^16 + 2032x^14 + 9356x^12 + 27824x^10 + 55136x^8 + 74080x^6 + 64960x^4 + 32000x^2 + 6400	\( 2^{28}\cdot 3^{12}\cdot 5^{12}\cdot 691^{4} \)	20T1025	Trivial (GRH)
20.8.9806875082992983948596343994140625.1	x^20 - 29x^18 - 42x^17 + 86x^16 + 116x^15 - 355x^14 + 64x^13 + 1478x^12 - 3556x^11 + 2434x^10 - 20912x^9 + 50641x^8 + 47430x^7 - 47925x^6 - 330770x^5 + 314185x^4 + 517250x^3 - 1007000x^2 + 594300x - 120475	\( 5^{16}\cdot 6329^{6} \)	20T1025	Trivial (GRH)
20.4.132894455303943784655361213134765625.1	x^20 - 5x^19 + 20x^18 - 118x^17 + 369x^16 - 1551x^15 + 1640x^14 + 2783x^13 - 1148x^12 + 25126x^11 - 47926x^10 + 2665x^9 + 27394x^8 + 207092x^7 - 182609x^6 - 41223x^5 + 236898x^4 + 586329x^3 - 180810x^2 - 42039x + 53181	\( 3^{12}\cdot 5^{12}\cdot 97^{2}\cdot 691^{6} \)	20T1025	Trivial (GRH)
20.12.4356355619334769553608704000000000000.1	x^20 - 26x^16 + 23x^14 + 171x^12 - 165x^10 - 425x^8 + 331x^6 + 362x^4 - 156x^2 + 9	\( 2^{24}\cdot 3^{2}\cdot 5^{12}\cdot 41^{4}\cdot 2543^{4} \)	20T1025	Trivial (GRH)
20.8.401987189260024679669760000000000000000.1	x^20 - 15x^18 + 75x^16 + 3190x^14 - 71880x^12 + 381000x^10 + 410000x^8 - 5256000x^6 - 2304000x^4 + 25920000x^2 + 12960000	\( 2^{28}\cdot 3^{16}\cdot 5^{16}\cdot 691^{4} \)	20T1025	Trivial (GRH)
20.12.612576255759573370734751264818904170496.1	x^20 - 8x^19 - 10x^18 + 244x^17 - 944x^16 - 1944x^15 + 27942x^14 - 20368x^13 - 296034x^12 + 626076x^11 + 572560x^10 - 4641000x^9 + 9733290x^8 + 567192x^7 - 33430872x^6 + 51004208x^5 - 65906436x^4 + 87451344x^3 - 46599072x^2 + 533536x + 63032	\( 2^{48}\cdot 31^{10}\cdot 227^{4} \)	20T1025	Trivial (GRH)
20.4.612576255759573370734751264818904170496.1	x^20 - 4x^19 + 54x^18 - 124x^17 + 1221x^16 - 1196x^15 + 7116x^14 + 1724x^13 - 50715x^12 + 110152x^11 - 180762x^10 - 274808x^9 + 766294x^8 - 4918480x^7 - 4021410x^6 + 25190444x^5 + 11339568x^4 + 23998572x^3 - 67507864x^2 - 68625992x + 3959762	\( 2^{48}\cdot 31^{10}\cdot 227^{4} \)	20T1025	$[2]$ (GRH)
20.8.612576255759573370734751264818904170496.1	x^20 - 8x^19 + 42x^18 - 316x^17 + 1343x^16 - 5704x^15 + 22066x^14 - 60828x^13 + 217183x^12 - 331524x^11 + 1185192x^10 - 823644x^9 + 3892137x^8 + 2160304x^7 + 1887716x^6 + 13096568x^5 - 34808130x^4 - 732960x^3 + 12280096x^2 + 1273344x - 369536	\( 2^{48}\cdot 31^{10}\cdot 227^{4} \)	20T1025	Trivial (GRH)
20.12.612576255759573370734751264818904170496.2	x^20 - 4x^19 - 44x^18 + 300x^17 - 623x^16 - 208x^15 + 15368x^14 - 114296x^13 + 472819x^12 - 1418768x^11 + 3158862x^10 - 4604316x^9 + 2157922x^8 + 13116408x^7 - 44511864x^6 + 41666720x^5 + 60019076x^4 - 102874864x^3 - 53866648x^2 + 7202352x + 3747704	\( 2^{48}\cdot 31^{10}\cdot 227^{4} \)	20T1025	Trivial (GRH)
20.16.2450305023038293482939005059275616681984.1	x^20 - 4x^19 - 8x^18 - 116x^17 - 765x^16 - 12x^15 + 14440x^14 + 106828x^13 + 295185x^12 - 70732x^11 - 1504642x^10 - 1333928x^9 + 2312296x^8 + 3361668x^7 - 1062072x^6 - 2870084x^5 - 204528x^4 + 837312x^3 + 116368x^2 - 64768x + 4178	\( 2^{50}\cdot 31^{10}\cdot 227^{4} \)	20T1025	Trivial (GRH)
20.0.7330834517590754249461342942057121972224.1	x^20 - 4x^19 + 62x^18 - 96x^17 + 1402x^16 + 520x^15 + 18452x^14 + 37728x^13 + 203669x^12 + 527812x^11 + 1772298x^10 + 4473144x^9 + 11402270x^8 + 24260480x^7 + 46631592x^6 + 72089680x^5 + 100842924x^4 + 108321624x^3 + 91010256x^2 + 53328976x + 31457276	\( 2^{50}\cdot 31^{4}\cdot 227^{8} \)	20T1025	$[2, 2, 29820]$ (GRH)
20.16.9801220092153173931756020237102466727936.1	x^20 - 86x^18 - 28x^17 + 2486x^16 + 3304x^15 - 17904x^14 - 134036x^13 - 431938x^12 + 2196536x^11 + 9178424x^10 - 7077232x^9 - 57112310x^8 - 207011648x^7 + 46964488x^6 + 2477753184x^5 + 468605560x^4 - 9649067552x^3 - 492654464x^2 + 10166002240x + 2125814384	\( 2^{52}\cdot 31^{10}\cdot 227^{4} \)	20T1025	Trivial (GRH)
20.4.43190884988844472906188100000000000000000000.1	x^20 + 50x^18 + 805x^16 + 1015x^14 - 105125x^12 - 1247232x^10 - 8229185x^8 - 48656055x^6 - 169747440x^4 + 594823321	\( 2^{20}\cdot 5^{20}\cdot 29^{10}\cdot 179^{4} \)	20T1025	$[2]$ (GRH)
20.0.43542784730387716079982562074992896000000000000.1	x^20 + 291x^18 + 34523x^16 + 2164086x^14 + 77860477x^12 + 1637220249x^10 + 19617373055x^8 + 123475672018x^6 + 342449474695x^4 + 347793632904x^2 + 34507149121	\( 2^{20}\cdot 5^{12}\cdot 257^{4}\cdot 431^{4}\cdot 1031^{4} \)	20T1025	$[2, 4, 25464776]$ (GRH)
20.20.8088551234301552526733640713612755353856000000000000.1	x^20 - 654x^18 + 182428x^16 - 28582758x^14 + 2783036051x^12 - 175645980387x^10 + 7257234585990x^8 - 193051166481831x^6 + 3145361149528271x^4 - 28079433439933088x^2 + 102561320445857296	\( 2^{20}\cdot 5^{12}\cdot 257^{4}\cdot 431^{6}\cdot 1031^{4} \)	20T1025	Trivial (GRH)
20.12.434073807522026850838993805941780627654560000000000000000.1	x^20 - 5680x^18 + 14020930x^16 - 19736095850x^14 + 17469170847825x^12 - 10102154439305000x^10 + 3834786993819768625x^8 - 933272710766328395625x^6 + 137377792648080355178125x^4 - 10873455887817253368515625x^2 + 349861680657101806869390625	\( 2^{20}\cdot 3^{12}\cdot 5^{16}\cdot 691^{4}\cdot 5309^{6} \)	20T1025	$[2]$ (GRH)