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 49 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.35301481425473668370514944.1	x^20 - 6x^19 + 19x^18 - 36x^17 + 21x^16 + 99x^15 - 360x^14 + 628x^13 - 540x^12 - 403x^11 + 1961x^10 - 3254x^9 + 3627x^8 - 2576x^7 + 2505x^6 - 3141x^5 + 3595x^4 - 2846x^3 + 1138x^2 - 678x + 443	\( 2^{10}\cdot 23^{3}\cdot 4903^{5} \)	20T993	Trivial (GRH)
20.0.35301481425473668370514944.2	x^20 - 6x^19 + 16x^18 - 40x^17 + 123x^16 - 333x^15 + 776x^14 - 1545x^13 + 2433x^12 - 3215x^11 + 3963x^10 - 4332x^9 + 4172x^8 - 3292x^7 + 1004x^6 + 288x^5 + 400x^4 - 288x^3 + 160x^2 + 32	\( 2^{10}\cdot 23^{3}\cdot 4903^{5} \)	20T993	Trivial (GRH)
20.2.196479881063110703847148051.1	x^20 - 4x^19 + 4x^18 + 16x^17 - 73x^16 + 84x^15 + 126x^14 - 491x^13 + 561x^12 + 218x^11 - 1497x^10 + 1666x^9 - 411x^8 - 1080x^7 + 2396x^6 - 2202x^5 + 416x^4 + 696x^3 - 1498x^2 + 1436x - 233	\( -\,37^{5}\cdot 4903^{5} \)	20T993	Trivial (GRH)
20.10.909556369822141985336351744.1	x^20 - 9x^19 + 30x^18 - 26x^17 - 92x^16 + 235x^15 - 38x^14 - 277x^13 - 443x^12 + 1550x^11 + 245x^10 - 4064x^9 + 3041x^8 + 2955x^7 - 4618x^6 + 302x^5 + 2054x^4 - 768x^3 - 178x^2 + 108x - 9	\( -\,2^{10}\cdot 71^{5}\cdot 281^{6} \)	20T993	Trivial (GRH)
20.6.909556369822141985336351744.1	x^20 + 3x^18 + x^16 + x^14 - 22x^12 - 101x^10 - 33x^8 + 204x^6 + 159x^4 - 71x^2 - 71	\( -\,2^{10}\cdot 71^{5}\cdot 281^{6} \)	20T993	Trivial (GRH)
20.10.909556369822141985336351744.2	x^20 + 6x^18 + 8x^16 - 89x^14 - 80x^12 + 257x^10 + 245x^8 - 512x^6 + 23x^4 + 213x^2 - 71	\( -\,2^{10}\cdot 71^{5}\cdot 281^{6} \)	20T993	Trivial (GRH)
20.6.909556369822141985336351744.2	x^20 - 2x^18 - 16x^16 + 13x^14 + 76x^12 - 43x^10 - 87x^8 + 500x^6 + 911x^4 + 355x^2 - 71	\( -\,2^{10}\cdot 71^{5}\cdot 281^{6} \)	20T993	Trivial (GRH)
20.2.150492394277306332649545007104.1	x^20 + 13x^18 + 30x^16 - 143x^14 - 510x^12 + 1753x^10 - 3507x^8 - 65361x^6 - 60193x^4 + 308889x^2 - 181411	\( -\,2^{20}\cdot 37^{3}\cdot 4903^{5} \)	20T993	Trivial (GRH)
20.4.235332335628288295024534224896.1	x^20 - 6x^19 + 22x^18 - 46x^17 + 63x^16 - 90x^15 + 129x^14 - 92x^13 - 422x^12 + 1474x^11 - 1091x^10 - 1548x^9 + 2480x^8 - 10x^7 - 1663x^6 + 758x^5 + 181x^4 + 34x^3 - 412x^2 + 330x - 91	\( 2^{20}\cdot 71^{6}\cdot 281^{5} \)	20T993	Trivial (GRH)
20.8.235332335628288295024534224896.1	x^20 - 2x^19 - 10x^18 + 26x^17 - 7x^16 - 190x^15 + 184x^14 + 726x^13 + 180x^12 - 986x^11 - 1890x^10 + 530x^9 + 2089x^8 + 236x^7 - 106x^6 - 722x^5 - 453x^4 + 264x^3 + 68x^2 - 6x + 1	\( 2^{20}\cdot 71^{6}\cdot 281^{5} \)	20T993	Trivial (GRH)
20.8.235332335628288295024534224896.2	x^20 - 6x^19 - 4x^18 + 46x^17 + 101x^16 - 142x^15 - 731x^14 - 904x^13 + 616x^12 + 3398x^11 + 4280x^10 + 760x^9 - 5100x^8 - 7784x^7 - 4899x^6 + 166x^5 + 2795x^4 + 2280x^3 + 883x^2 + 156x + 9	\( 2^{20}\cdot 71^{6}\cdot 281^{5} \)	20T993	Trivial (GRH)
20.0.360211787453875796266594598912.1	x^20 + 10x^18 + 77x^16 + 666x^14 + 3940x^12 + 16389x^10 + 57852x^8 + 160142x^6 + 313230x^4 + 510053x^2 + 510053	\( 2^{20}\cdot 317^{3}\cdot 1609^{5} \)	20T993	Trivial (GRH)
20.4.360211787453875796266594598912.1	x^20 + 6x^18 - 8x^16 - 52x^14 - 1307x^12 - 9565x^10 + 10196x^8 + 124825x^6 - 65207x^4 - 510053x^2 + 510053	\( 2^{20}\cdot 317^{3}\cdot 1609^{5} \)	20T993	Trivial (GRH)
20.0.360211787453875796266594598912.2	x^20 + 11x^18 + 93x^16 + 642x^14 + 3205x^12 + 13655x^10 + 48373x^8 + 131635x^6 + 291778x^4 + 510053x^2 + 510053	\( 2^{20}\cdot 317^{3}\cdot 1609^{5} \)	20T993	Trivial (GRH)
20.4.360211787453875796266594598912.2	x^20 - 5x^18 - 9x^16 + 83x^14 + x^12 - 2832x^10 - 17183x^8 - 98647x^6 - 152766x^4 - 510053x^2 + 510053	\( 2^{20}\cdot 317^{3}\cdot 1609^{5} \)	20T993	Trivial (GRH)
20.0.532759812203551559843606167552.1	x^20 + 13x^18 + 87x^16 + 393x^14 + 1242x^12 + 2733x^10 + 4247x^8 + 4752x^6 + 3734x^4 + 1818x^2 + 397	\( 2^{20}\cdot 61^{6}\cdot 397^{5} \)	20T993	Trivial (GRH)
20.12.532759812203551559843606167552.1	x^20 - 13x^18 + 76x^16 - 299x^14 + 805x^12 - 1206x^10 + 1005x^8 - 1317x^6 + 2347x^4 - 1821x^2 + 397	\( 2^{20}\cdot 61^{6}\cdot 397^{5} \)	20T993	Trivial (GRH)
20.4.532759812203551559843606167552.1	x^20 + x^18 - 25x^16 - 127x^14 - 375x^12 - 557x^10 - 449x^8 + 206x^6 + 1532x^4 + 1557x^2 + 397	\( 2^{20}\cdot 61^{6}\cdot 397^{5} \)	20T993	Trivial (GRH)
20.8.532759812203551559843606167552.1	x^20 - 9x^18 + 37x^16 - 103x^14 + 131x^12 + 585x^10 - 2414x^8 + 1183x^6 + 3078x^4 - 2609x^2 + 397	\( 2^{20}\cdot 61^{6}\cdot 397^{5} \)	20T993	Trivial (GRH)
20.0.532759812203551559843606167552.2	x^20 + 13x^18 + 76x^16 + 299x^14 + 805x^12 + 1206x^10 + 1005x^8 + 1317x^6 + 2347x^4 + 1821x^2 + 397	\( 2^{20}\cdot 61^{6}\cdot 397^{5} \)	20T993	Trivial (GRH)
20.12.532759812203551559843606167552.2	x^20 - 13x^18 + 87x^16 - 393x^14 + 1242x^12 - 2733x^10 + 4247x^8 - 4752x^6 + 3734x^4 - 1818x^2 + 397	\( 2^{20}\cdot 61^{6}\cdot 397^{5} \)	20T993	Trivial (GRH)
20.4.532759812203551559843606167552.2	x^20 + 3x^18 - 4x^16 - 11x^14 + 30x^12 + 18x^10 - 702x^8 - 907x^6 + 594x^4 + 1212x^2 + 397	\( 2^{20}\cdot 61^{6}\cdot 397^{5} \)	20T993	Trivial (GRH)
20.8.532759812203551559843606167552.2	x^20 - 9x^18 + 11x^16 + 139x^14 - 688x^12 + 1507x^10 - 2190x^8 + 2383x^6 - 816x^4 - 706x^2 + 397	\( 2^{20}\cdot 61^{6}\cdot 397^{5} \)	20T993	Trivial (GRH)
20.2.931385722697873392984424185856.1	x^20 + 12x^18 + 44x^16 + 27x^14 - 186x^12 - 579x^10 - 1031x^8 - 1032x^6 - 129x^4 + 213x^2 - 71	\( -\,2^{20}\cdot 71^{5}\cdot 281^{6} \)	20T993	Trivial (GRH)
20.6.931385722697873392984424185856.1	x^20 - 15x^18 + 89x^16 - 260x^14 + 323x^12 + 173x^10 - 914x^8 + 745x^6 - 202x^4 - 426x^2 - 71	\( -\,2^{20}\cdot 71^{5}\cdot 281^{6} \)	20T993	Trivial (GRH)
20.2.931385722697873392984424185856.2	x^20 + 3x^16 + 49x^14 - 11x^12 - 224x^10 - 266x^8 - 583x^6 - 808x^4 - 426x^2 - 71	\( -\,2^{20}\cdot 71^{5}\cdot 281^{6} \)	20T993	Trivial (GRH)
20.6.931385722697873392984424185856.2	x^20 - 7x^18 - 4x^16 + 77x^14 - 150x^12 - 156x^10 + 702x^8 + 426x^6 - 238x^4 - 213x^2 - 71	\( -\,2^{20}\cdot 71^{5}\cdot 281^{6} \)	20T993	Trivial (GRH)
20.4.963340856852431780962566894053.1	x^20 - 8x^19 + 30x^18 - 59x^17 + 49x^16 + 16x^15 + 66x^14 - 587x^13 + 945x^12 + 1040x^11 - 6509x^10 + 11468x^9 - 9273x^8 + 1254x^7 + 3747x^6 - 2210x^5 - 782x^4 + 853x^3 + 212x^2 - 157x - 23	\( 37^{5}\cdot 4903^{6} \)	20T993	Trivial (GRH)
20.0.240980311683367214105123046293504.1	x^20 - 10x^19 + 54x^18 - 162x^17 + 177x^16 + 868x^15 - 5252x^14 + 14484x^13 - 20590x^12 - 5896x^11 + 114696x^10 - 340360x^9 + 652002x^8 - 935412x^7 + 1058596x^6 - 966276x^5 + 721101x^4 - 426750x^3 + 192610x^2 - 57606x + 9837	\( 2^{30}\cdot 71^{6}\cdot 281^{5} \)	20T993	$[2]$ (GRH)
20.4.240980311683367214105123046293504.1	x^20 - 6x^18 - 19x^16 + 282x^14 - 1368x^12 - 756x^10 + 1699x^8 - 17066x^6 - 22217x^4 + 2810x^2 + 281	\( 2^{30}\cdot 71^{6}\cdot 281^{5} \)	20T993	Trivial (GRH)
20.0.240980311683367214105123046293504.2	x^20 - 2x^19 + 18x^18 - 18x^17 + 144x^16 - 154x^15 + 794x^14 - 572x^13 + 2594x^12 - 850x^11 + 5796x^10 + 48x^9 + 515x^8 + 12248x^7 - 2970x^6 + 3678x^5 - 7890x^4 - 1282x^3 + 8296x^2 - 5016x + 1201	\( 2^{30}\cdot 71^{6}\cdot 281^{5} \)	20T993	$[2]$ (GRH)
20.2.694395645719143833909599927271424.1	x^20 + 20x^18 + 91x^16 - 250x^14 - 3767x^12 + 4008x^10 - 32081x^8 - 776602x^6 - 401493x^4 + 1051823x^2 - 1041331	\( -\,2^{20}\cdot 43^{3}\cdot 61^{5}\cdot 397^{5} \)	20T993	Trivial (GRH)
20.6.694395645719143833909599927271424.1	x^20 + 6x^18 - 54x^16 - 847x^14 + 36x^12 - 8340x^10 + 52576x^8 + 250251x^6 - 310654x^4 + 527223x^2 - 1041331	\( -\,2^{20}\cdot 43^{3}\cdot 61^{5}\cdot 397^{5} \)	20T993	Trivial (GRH)
20.2.694395645719143833909599927271424.2	x^20 + 2x^18 + 57x^16 - 21x^14 - 2879x^12 - 3437x^10 - 22983x^8 - 60821x^6 + 193540x^4 - 18361x^2 - 1041331	\( -\,2^{20}\cdot 43^{3}\cdot 61^{5}\cdot 397^{5} \)	20T993	Trivial (GRH)
20.6.694395645719143833909599927271424.2	x^20 + 10x^18 - 101x^16 - 927x^14 + 2564x^12 + 27904x^10 - 5182x^8 - 297562x^6 - 180503x^4 + 1447896x^2 - 1041331	\( -\,2^{20}\cdot 43^{3}\cdot 61^{5}\cdot 397^{5} \)	20T993	Trivial (GRH)
20.16.3550520998942383746231172591517696.1	x^20 - 26x^18 + 199x^16 + 116x^14 - 7649x^12 + 26800x^10 + 3295x^8 - 110218x^6 + 73582x^4 - 4148x^2 + 61	\( 2^{30}\cdot 61^{5}\cdot 397^{6} \)	20T993	Trivial (GRH)
20.4.3550520998942383746231172591517696.1	x^20 - 4x^19 + 66x^17 - 296x^16 + 128x^15 + 1930x^14 - 3094x^13 - 3878x^12 + 10740x^11 - 2802x^10 - 4148x^9 + 19635x^8 - 62956x^7 + 4884x^6 + 178202x^5 - 196672x^4 + 6778x^3 + 159750x^2 - 217446x + 116005	\( 2^{30}\cdot 61^{5}\cdot 397^{6} \)	20T993	Trivial (GRH)
20.16.3550520998942383746231172591517696.2	x^20 - 4x^19 - 18x^18 + 42x^17 + 145x^16 + 162x^15 - 1070x^14 - 3576x^13 + 7575x^12 + 13658x^11 - 30898x^10 + 52x^9 + 46602x^8 - 96486x^7 + 40934x^6 + 176374x^5 - 168771x^4 - 88034x^3 + 110372x^2 + 13436x - 20281	\( 2^{30}\cdot 61^{5}\cdot 397^{6} \)	20T993	Trivial (GRH)
20.4.3550520998942383746231172591517696.2	x^20 + 26x^18 + 199x^16 - 116x^14 - 7649x^12 - 26800x^10 + 3295x^8 + 110218x^6 + 73582x^4 + 4148x^2 + 61	\( 2^{30}\cdot 61^{5}\cdot 397^{6} \)	20T993	Trivial (GRH)
20.4.755572950161032139756256429906853888.1	x^20 - 10x^18 + 67x^16 + 110x^14 + 3971x^12 + 37680x^10 - 1069256x^8 + 4472194x^6 + 23917905x^4 - 165224430x^2 + 228115693	\( 2^{30}\cdot 37^{3}\cdot 4903^{6} \)	20T993	Trivial (GRH)
20.10.17219767656837638375207712193261644808192.1	x^20 + 22x^18 - 615x^16 - 2194x^14 + 7936x^12 + 271440x^10 + 4275523x^8 + 3531310x^6 - 2501381x^4 + 347526x^2 - 12427	\( -\,2^{30}\cdot 43^{3}\cdot 61^{6}\cdot 397^{6} \)	20T993	Trivial (GRH)
20.6.17219767656837638375207712193261644808192.1	x^20 - 16x^18 - 58x^16 + 6808x^14 - 135475x^12 - 797014x^10 + 8314592x^8 + 24367286x^6 - 37935244x^4 - 134241700x^2 - 71445403	\( -\,2^{30}\cdot 43^{3}\cdot 61^{6}\cdot 397^{6} \)	20T993	Trivial (GRH)
20.10.17219767656837638375207712193261644808192.2	x^20 + 20x^18 - 6x^16 - 3284x^14 - 153267x^12 - 776418x^10 + 11224728x^8 - 19017278x^6 + 7392720x^4 - 649988x^2 - 12427	\( -\,2^{30}\cdot 43^{3}\cdot 61^{6}\cdot 397^{6} \)	20T993	Trivial (GRH)
20.6.17219767656837638375207712193261644808192.2	x^20 + 4x^18 - 488x^16 + 502x^14 + 51996x^12 - 535382x^10 + 1131717x^8 + 28080744x^6 - 124966870x^4 - 203200112x^2 - 71445403	\( -\,2^{30}\cdot 43^{3}\cdot 61^{6}\cdot 397^{6} \)	20T993	Trivial (GRH)
20.10.634489950985999984940133256223865794519711.1	x^20 - 4x^19 - 97x^18 - 370x^17 - 6187x^16 + 33002x^15 + 497168x^14 + 3038916x^13 + 20947096x^12 + 79881242x^11 + 56317635x^10 + 211378009x^9 + 6767525693x^8 - 111639824098x^7 + 68408260032x^6 - 1964963804865x^5 - 3739321671269x^4 + 39767820622220x^3 + 6968832674831x^2 - 69114537885447x - 25230707491711	\( -\,61^{7}\cdot 167^{5}\cdot 397^{7} \)	20T993	$[2]$ (GRH)
20.12.1882683124603340346737834393885030954619199578692919831281.1	x^20 - 5x^19 - 437x^18 + 4845x^17 + 56275x^16 - 1250245x^15 + 2649064x^14 + 112224094x^13 - 1128990753x^12 + 656158961x^11 + 65065091965x^10 - 541445137114x^9 + 1289614208260x^8 + 10399205575195x^7 - 118954685062451x^6 + 619329195312958x^5 - 2061700573769882x^4 + 4641260420923903x^3 - 6920118181161654x^2 + 6226784919992940x - 2576448204562511	\( 53^{3}\cdot 61^{5}\cdot 397^{5}\cdot 11493420709^{3} \)	20T993	$[2]$ (GRH)
20.12.8115473275425993676513111964179251562561388243938577254913.1	x^20 - 533x^18 - 4034x^17 + 92064x^16 + 1479745x^15 - 375986x^14 - 169175375x^13 - 1373161083x^12 + 1665336900x^11 + 102020618143x^10 + 733101651678x^9 + 1187534134673x^8 - 18774067823277x^7 - 184077684732574x^6 - 916247209555166x^5 - 2978358234313399x^4 - 6600332540709378x^3 - 9726583452943970x^2 - 8669600655269047x - 3558137714849521	\( 13^{6}\cdot 61^{5}\cdot 397^{5}\cdot 709^{3}\cdot 8273789^{3} \)	20T993	$[2, 2]$ (GRH)
20.4.45592937228519093176950135516713794628013156197206439554131977.1	x^20 - 10x^19 - 551x^18 + 5244x^17 + 143308x^16 - 1266620x^15 - 23396286x^14 + 186362336x^13 + 2659716342x^12 - 18440210056x^11 - 220124145524x^10 + 1274252880396x^9 + 13432422281717x^8 - 61585942496134x^7 - 597010337880175x^6 + 2012144808234700x^5 + 18523626732012672x^4 - 40475332525530080x^3 - 363645477908500760x^2 + 384229164241789480x + 3464377612615374383	\( 53^{3}\cdot 61^{6}\cdot 397^{6}\cdot 11493420709^{3} \)	20T993	$[2, 408]$ (GRH)
20.20.9929433642609894647025299066458363139771040828879729378027092224.1	x^20 - 6x^19 - 733x^18 + 7741x^17 + 188719x^16 - 3182866x^15 - 12476856x^14 + 549338388x^13 - 2553611132x^12 - 31840073023x^11 + 427700051966x^10 - 1315604444133x^9 - 10781962773608x^8 + 135434048622884x^7 - 725209750505368x^6 + 2398520109440166x^5 - 5273329729744581x^4 + 7747006836663003x^3 - 7320465920773089x^2 + 4024806585247686x - 978037072568503	\( 2^{8}\cdot 109^{3}\cdot 33769^{5}\cdot 88024724149^{3} \)	20T993	$[2]$ (GRH)