Global number field search results

Further refine search

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 814)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.3125000000000000000000000000000000.1	x^20 + 40x^18 + 680x^16 + 6400x^14 + 36400x^12 + 128160x^10 + 275200x^8 + 342400x^6 + 224000x^4 + 64000x^2 + 5120	\( 2^{30}\cdot 5^{35} \)	$C_{20}$ (as 20T1)	$[1202]$ (GRH)
20.0.3408472966438093473521603359801344.1	x^20 + 29x^18 + 368x^16 + 2686x^14 + 12466x^12 + 38378x^10 + 79259x^8 + 108301x^6 + 93630x^4 + 46230x^2 + 9901	\( 2^{20}\cdot 3^{10}\cdot 11^{18}\cdot 9901 \)	20T409	$[2, 690]$ (GRH)
20.0.3726089326485790135900160000000000.1	x^20 + 31x^18 + 419x^16 + 3244x^14 + 15880x^12 + 51113x^10 + 108761x^8 + 149291x^6 + 123804x^4 + 53436x^2 + 7919	\( 2^{20}\cdot 5^{10}\cdot 11^{16}\cdot 7919 \)	20T409	$[1672]$ (GRH)
20.0.6299663938062363808000000000000000.1	x^20 + 25x^18 + 271x^16 + 1670x^14 + 6444x^12 + 16160x^10 + 26445x^8 + 27575x^6 + 17275x^4 + 5750x^2 + 745	\( 2^{20}\cdot 5^{15}\cdot 149\cdot 6029^{4} \)	20T887	$[2, 520]$ (GRH)
20.0.9116864842110232195020398925971456.1	x^20 + 29x^18 + 361x^16 + 2539x^14 + 11180x^12 + 32258x^10 + 61918x^8 + 78302x^6 + 62633x^4 + 28705x^2 + 5741	\( 2^{20}\cdot 11^{16}\cdot 5741^{3} \)	20T335	$[1762]$ (GRH)
20.0.10019151533337487082567413330078125.1	x^20 - x^19 + 35x^18 - 36x^17 + 500x^16 - 536x^15 + 3874x^14 - 4410x^13 + 18734x^12 - 23144x^11 + 64285x^10 - 88253x^9 + 181094x^8 - 254178x^7 + 456689x^6 - 492583x^5 + 958226x^4 - 411001x^3 + 1371042x^2 + 173262x + 1197901	\( 3^{10}\cdot 5^{15}\cdot 11^{18} \)	$C_{20}$ (as 20T1)	$[2, 2, 842]$ (GRH)
20.0.12569066605710630176407970532818944.1	x^20 - 4x^19 + 32x^18 + 6x^17 + 202x^16 + 938x^15 + 1790x^14 + 5494x^13 + 12527x^12 + 17820x^11 + 50458x^10 + 56452x^9 + 119267x^8 + 113984x^7 + 353348x^6 + 19962x^5 + 844391x^4 - 209964x^3 + 1076236x^2 - 150400x + 539177	\( 2^{30}\cdot 11^{18}\cdot 1451^{2} \)	20T340	$[2, 850]$ (GRH)
20.0.12569066605710630176407970532818944.2	x^20 - 6x^19 + 28x^18 - 54x^17 + 56x^16 + 184x^15 + 1638x^14 - 16140x^13 + 84550x^12 - 301356x^11 + 842392x^10 - 1926386x^9 + 3717519x^8 - 6131704x^7 + 8726846x^6 - 10659646x^5 + 11152518x^4 - 9762542x^3 + 6937796x^2 - 3721474x + 1233541	\( 2^{30}\cdot 11^{18}\cdot 1451^{2} \)	20T340	$[2, 878]$ (GRH)
20.0.13936805290105078002151559671054336.6	x^20 - 6x^19 - 3x^18 + 76x^17 + 6x^16 - 716x^15 + 1124x^14 + 746x^13 - 1614x^12 - 3738x^11 + 31152x^10 - 64886x^9 + 160716x^8 - 233920x^7 + 672301x^6 - 960348x^5 + 2267144x^4 - 2279050x^3 + 3509093x^2 - 1817414x + 1908103	\( 2^{30}\cdot 7^{10}\cdot 11^{16} \)	$C_2\times C_{10}$ (as 20T3)	$[11, 110]$ (GRH)
20.0.15097568161436356604099273681640625.2	x^20 - 10x^19 + 55x^18 - 210x^17 + 715x^16 - 2250x^15 + 6655x^14 - 17485x^13 + 43615x^12 - 99585x^11 + 218518x^10 - 432640x^9 + 837095x^8 - 1427265x^7 + 2414710x^6 - 3425825x^5 + 4994295x^4 - 5360940x^3 + 6692935x^2 - 4116040x + 4451401	\( 5^{34}\cdot 11^{10} \)	$C_2\times C_{10}$ (as 20T3)	$[5, 710]$ (GRH)
20.0.18892144330291821549352960000000000.1	x^20 + 44x^18 + 646x^16 + 4788x^14 + 20635x^12 + 54632x^10 + 89857x^8 + 89868x^6 + 51571x^4 + 15088x^2 + 1699	\( 2^{20}\cdot 5^{10}\cdot 19^{4}\cdot 1699^{5} \)	20T168	$[1246]$ (GRH)
20.0.19280067292868642604792128836993024.1	x^20 + 32x^18 + 424x^16 + 3097x^14 + 13945x^12 + 40764x^10 + 78842x^8 + 100146x^6 + 80304x^4 + 36845x^2 + 7369	\( 2^{20}\cdot 11^{16}\cdot 7369^{3} \)	20T335	$[2, 1090]$ (GRH)
20.0.20213777905110009806334605947265625.1	x^20 - 4x^19 + 34x^18 - 96x^17 + 337x^16 - 610x^15 + 1271x^14 - 1037x^13 + 2070x^12 + 2371x^11 + 5375x^10 + 6616x^9 + 42851x^8 - 19136x^7 + 183155x^6 - 111821x^5 + 401105x^4 - 200424x^3 + 487862x^2 - 125820x + 297859	\( 3^{10}\cdot 5^{10}\cdot 19^{5}\cdot 1699^{5} \)	$C_2\times D_5\wr C_2$ (as 20T92)	$[2, 1116]$ (GRH)
20.0.30368554900942376860763008296271249.1	x^20 - 6x^19 + 35x^18 - 136x^17 + 507x^16 - 1636x^15 + 4193x^14 - 9518x^13 + 16756x^12 - 26648x^11 + 37971x^10 - 87050x^9 + 575097x^8 - 2617976x^7 + 8187004x^6 - 18484780x^5 + 31602475x^4 - 41598580x^3 + 40346065x^2 - 25841940x + 8429607	\( 7^{10}\cdot 401^{10} \)	$D_{10}$ (as 20T4)	$[3, 3, 3, 78]$ (GRH)
20.0.32923153726536964440064000000000000.1	x^20 + 47x^18 + 943x^16 + 10586x^14 + 73265x^12 + 324649x^10 + 924049x^8 + 1640170x^6 + 1676815x^4 + 810375x^2 + 86725	\( 2^{28}\cdot 5^{12}\cdot 3469^{5} \)	20T756	$[2, 840]$ (GRH)
20.0.36453470746082782752000000000000000.1	x^20 + 42x^18 + 728x^16 + 6772x^14 + 36846x^12 + 120125x^10 + 231910x^8 + 254205x^6 + 146895x^4 + 40050x^2 + 4005	\( 2^{20}\cdot 3^{6}\cdot 5^{15}\cdot 23^{4}\cdot 89^{5} \)	20T887	$[2, 2, 582]$ (GRH)
20.0.43245808601363782342974430143053824.1	x^20 - 16x^18 + 26x^16 - 936x^14 + 17713x^12 + 1048x^10 + 159924x^8 - 319648x^6 + 499776x^4 + 910336x^2 + 1048576	\( 2^{20}\cdot 727^{10} \)	$D_{10}$ (as 20T4)	$[11, 143]$ (GRH)
20.0.43334575336354588934400000000000000.1	x^20 + 49x^18 + 904x^16 + 8724x^14 + 49997x^12 + 179735x^10 + 410473x^8 + 580023x^6 + 465228x^4 + 166014x^2 + 4761	\( 2^{20}\cdot 3^{6}\cdot 5^{14}\cdot 23^{6}\cdot 89^{4} \)	20T794	$[2, 1036]$ (GRH)
20.0.45205160142537061919431122643582976.1	x^20 + 43x^18 + 789x^16 + 8096x^14 + 51031x^12 + 203861x^10 + 512574x^8 + 776893x^6 + 648220x^4 + 252630x^2 + 32481	\( 2^{20}\cdot 401^{11} \)	$(C_2\times C_2^4:C_5).C_2$ (as 20T84)	$[2, 1066]$ (GRH)
20.0.45259984731914299465343386928991081.3	x^20 - x^19 + 57x^18 - 47x^17 + 1358x^16 - 888x^15 + 17602x^14 - 8722x^13 + 135642x^12 - 48422x^11 + 637946x^10 - 144089x^9 + 1791648x^8 - 32737x^7 + 2757163x^6 + 1386459x^5 + 2003270x^4 + 4167463x^3 - 383733x^2 + 1641938x + 9340321	\( 3^{10}\cdot 11^{18}\cdot 13^{10} \)	$C_2\times C_{10}$ (as 20T3)	$[5, 1100]$ (GRH)
20.0.58299958569124301174210560000000000.5	x^20 - 2x^19 + 5x^18 - 12x^17 + 106x^16 - 224x^15 + 378x^14 - 980x^13 + 4758x^12 - 10496x^11 + 16774x^10 - 43646x^9 + 150453x^8 - 296394x^7 + 579913x^6 - 598132x^5 + 2282848x^4 - 720158x^3 + 2512812x^2 + 1333444x + 1916641	\( 2^{30}\cdot 5^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	$[1464]$ (GRH)
20.0.58299958569124301174210560000000000.8	x^20 - 10x^19 + 79x^18 - 426x^17 + 2029x^16 - 7868x^15 + 27546x^14 - 82468x^13 + 225633x^12 - 539374x^11 + 1180345x^10 - 2260566x^9 + 3977799x^8 - 6099092x^7 + 8535738x^6 - 10101132x^5 + 11433163x^4 - 10442226x^3 + 8662447x^2 - 4511618x + 8823079	\( 2^{30}\cdot 5^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	$[2, 4026]$ (GRH)
20.0.72098801162275858741260523848334336.1	x^20 - 5x^19 + 21x^18 - 27x^17 + 111x^16 - 259x^15 + 253x^14 - 95x^13 + 1552x^12 + 672x^11 + 3307x^10 + 7274x^9 + 32883x^8 + 76288x^7 + 224448x^6 + 456093x^5 + 786619x^4 + 872615x^3 + 686603x^2 + 258966x + 49111	\( 2^{10}\cdot 31^{3}\cdot 36497^{6} \)	20T365	$[2, 644]$ (GRH)
20.0.92823398950633472182737117276798976.1	x^20 + 31x^18 + 398x^16 + 2833x^14 + 12506x^12 + 36026x^10 + 68956x^8 + 86978x^6 + 69452x^4 + 31805x^2 + 6361	\( 2^{20}\cdot 61^{4}\cdot 397^{4}\cdot 6361^{3} \)	20T791	$[38, 76]$ (GRH)
20.0.93878033821762240604784858628096000.1	x^20 + 30x^18 + 383x^16 + 2742x^14 + 12217x^12 + 35517x^10 + 68497x^8 + 86874x^6 + 69606x^4 + 31925x^2 + 6385	\( 2^{20}\cdot 5^{3}\cdot 61^{4}\cdot 397^{4}\cdot 1277^{3} \)	20T791	$[2, 10, 170]$ (GRH)
20.0.99230781955913713241292800000000000.1	x^20 + 25x^18 + 268x^16 + 1613x^14 + 5989x^12 + 14177x^10 + 21323x^8 + 19642x^6 + 10226x^4 + 2590x^2 + 245	\( 2^{32}\cdot 5^{11}\cdot 7^{2}\cdot 23^{4}\cdot 431^{4} \)	20T802	$[2, 2, 476]$ (GRH)
20.0.105354091924918286208204800000000000.1	x^20 + 50x^18 + 1073x^16 + 12924x^14 + 95854x^12 + 451496x^10 + 1341646x^8 + 2405876x^6 + 2340241x^4 + 936630x^2 + 17345	\( 2^{32}\cdot 5^{11}\cdot 3469^{5} \)	20T771	$[2, 1232]$ (GRH)
20.0.112385254718210608313247485941252096.1	x^20 + 37x^18 + 532x^16 + 3825x^14 + 14809x^12 + 30961x^10 + 33577x^8 + 18297x^6 + 4576x^4 + 385x^2 + 1	\( 2^{20}\cdot 41^{18} \)	$C_2\times C_{10}$ (as 20T3)	$[1420]$ (GRH)
20.0.115436618418847759115953789493837824.3	x^20 - 4x^19 - 16x^18 + 12x^17 + 222x^16 + 378x^15 + 1750x^14 + 4112x^13 + 13433x^12 + 23190x^11 + 70881x^10 + 89262x^9 + 287947x^8 + 230252x^7 + 856214x^6 + 418974x^5 + 1783158x^4 + 462756x^3 + 2333308x^2 + 204212x + 1497569	\( 2^{30}\cdot 401^{10} \)	$D_{10}$ (as 20T4)	$[29, 174]$ (GRH)
20.0.120158054683860237850976148859242769.2	x^20 - x^19 - 10x^18 + 21x^17 + 89x^16 - 320x^15 - 659x^14 + 4179x^13 + 3070x^12 - 49039x^11 + 15269x^10 - 539429x^9 + 371470x^8 + 5562249x^7 - 9648419x^6 - 51536320x^5 + 157668929x^4 + 409230591x^3 - 2143588810x^2 - 2357947691x + 25937424601	\( 11^{18}\cdot 43^{10} \)	$C_2\times C_{10}$ (as 20T3)	$[2, 2, 10, 30]$ (GRH)
20.0.133508811261782548210805849619140625.2	x^20 - 2x^19 + 37x^18 - 84x^17 + 462x^16 - 1512x^15 + 6553x^14 - 19235x^13 + 53719x^12 - 127455x^11 + 279153x^10 - 481338x^9 + 653452x^8 - 587336x^7 + 244207x^6 + 48357x^5 + 19266x^4 - 221220x^3 + 224100x^2 - 91125x + 18225	\( 3^{10}\cdot 5^{10}\cdot 7^{10}\cdot 31^{10} \)	$D_{10}$ (as 20T4)	$[22, 88]$ (GRH)
20.0.133508811261782548210805849619140625.3	x^20 - 10x^19 + 53x^18 - 192x^17 + 905x^16 - 4180x^15 + 18294x^14 - 63680x^13 + 184128x^12 - 435736x^11 + 853479x^10 - 1378339x^9 + 1781990x^8 - 1790508x^7 + 1187558x^6 - 237809x^5 - 409139x^4 + 467764x^3 + 269196x^2 - 443775x + 562195	\( 3^{10}\cdot 5^{10}\cdot 7^{10}\cdot 31^{10} \)	$D_{10}$ (as 20T4)	$[2, 22, 88]$ (GRH)
20.0.133508811261782548210805849619140625.5	x^20 - 6x^19 + 53x^18 - 244x^17 + 1120x^16 - 4124x^15 + 13097x^14 - 38851x^13 + 99874x^12 - 235835x^11 + 542891x^10 - 1054816x^9 + 2110378x^8 - 3724529x^7 + 5617475x^6 - 8122839x^5 + 9109972x^4 - 4728816x^3 - 423366x^2 - 409185x + 2141055	\( 3^{10}\cdot 5^{10}\cdot 7^{10}\cdot 31^{10} \)	$D_{10}$ (as 20T4)	$[2, 22, 66]$ (GRH)
20.0.143685904663725311070484819161855201.1	x^20 - 6x^18 + 26x^16 - 222x^15 + 330x^14 + 690x^13 - 1266x^12 - 1920x^11 + 25630x^10 - 101226x^9 + 139181x^8 - 84090x^7 + 184336x^6 - 197640x^5 + 2009536x^4 - 4678560x^3 + 5809600x^2 - 5184000x + 2560000	\( 3^{10}\cdot 1093^{10} \)	$D_{10}$ (as 20T4)	$[11, 286]$ (GRH)
20.0.145671521378968039543605010986328125.1	x^20 + 44x^18 - 37x^17 + 769x^16 - 1799x^15 + 8136x^14 - 27411x^13 + 76643x^12 - 217497x^11 + 553045x^10 - 1184443x^9 + 2527476x^8 - 4505558x^7 + 7673064x^6 - 12834474x^5 + 19281736x^4 - 24949939x^3 + 27457237x^2 - 17683985x + 5729201	\( 3^{6}\cdot 5^{15}\cdot 23^{6}\cdot 89^{7} \)	20T466	$[2, 2, 1156]$ (GRH)
20.0.158263590809746088460400640000000000.1	x^20 - 2x^19 + 16x^18 - 22x^17 + 251x^16 - 312x^15 + 2463x^14 - 2000x^13 + 19766x^12 - 13838x^11 + 120498x^10 - 55698x^9 + 586287x^8 - 253640x^7 + 2275221x^6 - 618928x^5 + 6380134x^4 - 1342832x^3 + 12643885x^2 - 2415578x + 11745679	\( 2^{20}\cdot 5^{10}\cdot 11^{7}\cdot 28162171^{2} \)	20T781	$[2, 4128]$ (GRH)
20.0.159321702103922125456276290645206016.1	x^20 + 29x^18 - 19x^17 + 363x^16 - 516x^15 + 2749x^14 - 6390x^13 + 16099x^12 - 42411x^11 + 81481x^10 - 182224x^9 + 268289x^8 - 501531x^7 + 774271x^6 - 713742x^5 + 1813853x^4 - 892260x^3 + 1346246x^2 - 1607848x + 1025807	\( 2^{10}\cdot 3^{2}\cdot 401^{12} \)	20T347	$[2, 2, 678]$ (GRH)
20.0.180203247070312500000000000000000000.1	x^20 + 60x^18 + 1530x^16 + 21600x^14 + 184275x^12 + 973215x^10 + 3134700x^8 + 5850225x^6 + 5740875x^4 + 2460375x^2 + 295245	\( 2^{20}\cdot 3^{10}\cdot 5^{35} \)	$C_{20}$ (as 20T1)	$[2, 4322]$ (GRH)
20.0.183904915634328585745158994451759104.1	x^20 - 5x^19 + 54x^18 - 316x^17 + 1826x^16 - 8897x^15 + 39894x^14 - 156656x^13 + 557433x^12 - 1787652x^11 + 5172726x^10 - 13325642x^9 + 30691226x^8 - 62199734x^7 + 109814668x^6 - 159859442x^5 + 187140141x^4 - 156275611x^3 + 91765744x^2 - 17366336x + 4729127	\( 2^{32}\cdot 83^{4}\cdot 983^{6} \)	20T673	$[2, 2, 1514]$ (GRH)
20.0.200317132330035063121671003054276608.1	x^20 + 44x^18 + 770x^16 + 6952x^14 + 35552x^12 + 107712x^10 + 196504x^8 + 212960x^6 + 129712x^4 + 38720x^2 + 3872	\( 2^{55}\cdot 11^{18} \)	$C_{20}$ (as 20T1)	$[2050]$ (GRH)
20.0.234321944131076465734400000000000000.1	x^20 + 27x^18 + 290x^16 + 1652x^14 + 5528x^12 + 11250x^10 + 13821x^8 + 9740x^6 + 3476x^4 + 459x^2 + 11	\( 2^{20}\cdot 5^{14}\cdot 11^{9}\cdot 353^{4} \)	20T658	$[2, 734]$ (GRH)
20.0.248449367204871171790001164427198464.1	x^20 + 61x^18 + 1490x^16 + 18957x^14 + 138307x^12 + 606888x^10 + 1622222x^8 + 2579588x^6 + 2259251x^4 + 897479x^2 + 81589	\( 2^{36}\cdot 83^{5}\cdot 983^{5} \)	20T965	$[2, 2, 2076]$ (GRH)
20.0.248449367204871171790001164427198464.2	x^20 + 54x^18 + 1156x^16 + 13130x^14 + 87987x^12 + 361804x^10 + 913230x^8 + 1371346x^6 + 1151133x^4 + 489534x^2 + 81589	\( 2^{36}\cdot 83^{5}\cdot 983^{5} \)	20T965	$[2, 2, 1924]$ (GRH)
20.0.254903851560926116768000000000000000.1	x^20 + 58x^18 + 1368x^16 + 16943x^14 + 119596x^12 + 495730x^10 + 1220435x^8 + 1754905x^6 + 1376210x^4 + 482320x^2 + 30145	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	$[2, 3332]$ (GRH)
20.0.254903851560926116768000000000000000.2	x^20 + 59x^18 + 1457x^16 + 19511x^14 + 153086x^12 + 707510x^10 + 1831320x^8 + 2368985x^6 + 1341665x^4 + 334180x^2 + 30145	\( 2^{20}\cdot 5^{15}\cdot 6029^{5} \)	20T797	$[2, 2964]$ (GRH)
20.0.289566370164792960363300896559333376.2	x^20 + 33x^18 + 409x^16 + 2432x^14 + 7555x^12 + 12737x^10 + 11753x^8 + 5700x^6 + 1297x^4 + 113x^2 + 1	\( 2^{36}\cdot 71^{6}\cdot 179^{6} \)	20T531	$[2, 620]$ (GRH)
20.0.293741053706240000000000000000000000.1	x^20 + 25x^18 + 265x^16 + 1570x^14 + 5745x^12 + 13497x^10 + 20435x^8 + 19410x^6 + 10815x^4 + 3065x^2 + 311	\( 2^{36}\cdot 5^{22}\cdot 7^{8}\cdot 311 \)	20T513	$[2128]$ (GRH)
20.0.337133094159738515866255360000000000.1	x^20 + 53x^18 + 1145x^16 + 13110x^14 + 86183x^12 + 329209x^10 + 712221x^8 + 836914x^6 + 480569x^4 + 100601x^2 + 3469	\( 2^{36}\cdot 5^{10}\cdot 3469^{5} \)	20T756	$[3694]$ (GRH)
20.0.350664337162127669847494428212890625.3	x^20 - 8x^19 + 40x^18 - 123x^17 + 384x^16 - 999x^15 + 3004x^14 - 4808x^13 + 15643x^12 - 57768x^11 + 122352x^10 + 32265x^9 + 387883x^8 - 2403755x^7 + 270769x^6 + 3283896x^5 + 15232524x^4 - 19717650x^3 - 19671525x^2 - 14233725x + 91872225	\( 3^{10}\cdot 5^{10}\cdot 239^{10} \)	$D_{10}$ (as 20T4)	$[10, 150]$ (GRH)
20.0.360977976896857923653306611918700544.1	x^20 + 44x^18 + 737x^16 + 5940x^14 + 24464x^12 + 52976x^10 + 63283x^8 + 42108x^6 + 14883x^4 + 2420x^2 + 121	\( 2^{40}\cdot 3^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	$[2, 1364]$ (GRH)