Number field search results

Results (1-50 of 64 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
45.15.174...691.1	x^45 - 12x^44 + 42x^43 + 36x^42 - 525x^41 + 702x^40 + 2050x^39 - 5802x^38 - 2832x^37 + 26919x^36 - 20811x^35 - 75546x^34 + 201699x^33 - 97125x^32 - 532302x^31 + 1289591x^30 - 477339x^29 - 2405610x^28 + 4128988x^27 - 1666824x^26 - 5259345x^25 + 9273382x^24 + 3749217x^23 - 15223818x^22 - 9661128x^21 + 33692574x^20 - 4282803x^19 - 38096273x^18 + 36480543x^17 - 14154921x^16 + 10925288x^15 - 437979x^14 - 36804246x^13 + 57064132x^12 - 25852146x^11 - 34300866x^10 + 48986404x^9 - 2084457x^8 - 23365995x^7 + 5433983x^6 + 5348430x^5 - 1230861x^4 - 665734x^3 + 68376x^2 + 38973x + 2969	$45$	[15,15]	$-\,3^{60}\cdot 11^{39}$	$2$	$34.57020859771022$			?	$S_3\times C_{15}$ (as 45T3)	trivial	$2$	$29$	$495912260998404300$
45.1.246...829.1	x^45 - x - 1	$45$	[1,22]	$29\cdot 41\cdot 1451\cdot 23184662326519\cdot 476883331418375569\cdot 12\!\cdots\!01$	$6$	$44.9916992758$			✓	$S_{45}$ (as 45T10923)	not computed	$2$	$22$
45.15.226...891.1	x^45 - 3x^44 + 19x^43 - 46x^42 + 57x^41 - 164x^40 - 1542x^39 + 2752x^38 - 13177x^37 + 27636x^36 - 5513x^35 + 194674x^34 - 95004x^33 + 1568504x^32 - 4411428x^31 + 7701411x^30 - 22788169x^29 + 356245x^28 + 13001022x^27 - 120681074x^26 + 379138834x^25 - 251876102x^24 + 576442931x^23 + 394617661x^22 - 1914308187x^21 + 1873927920x^20 - 5326366508x^19 + 1371219529x^18 + 2001539759x^17 - 9889048234x^16 + 22330230077x^15 - 9918095549x^14 + 1934927850x^13 + 41001461054x^12 - 37979697765x^11 + 8169529015x^10 + 13175783912x^9 - 55418628407x^8 + 2188320806x^7 - 1793697518x^6 - 21729183123x^5 - 927541692x^4 + 301468299x^3 + 1484196634x^2 + 59977427x - 879691	$45$	[15,15]	$-\,11^{39}\cdot 31^{30}$	$2$	$78.84632509790313$			?	$S_3\times C_{15}$ (as 45T3)	not computed	$2$	$29$
45.1.421...456.1	x^45 - 4x - 4	$45$	[1,22]	$2^{44}\cdot 61\cdot 6357179\cdot 171802225249\cdot 418161846581\cdot 8092657633001\cdot 14050885843711\cdot 75717538318411921$	$8$	$88.5581252469$			?	$S_{45}$ (as 45T10923)	not computed	$2$	$22$
45.1.429...728.1	x^45 - 2x - 2	$45$	[1,22]	$2^{44}\cdot 79\cdot 1013\cdot 30\!\cdots\!79$	$4$	$88.5914985881$			✓	$S_{45}$ (as 45T10923)	not computed	$2$	$22$
45.1.436...704.1	x^45 - x - 2	$45$	[1,22]	$2^{44}\cdot 24\!\cdots\!69$	$2$	$88.6243277641$			✓	$S_{45}$ (as 45T10923)	not computed	$2$	$22$
45.1.436...000.1	x^45 - 2	$45$	[1,22]	$2^{44}\cdot 3^{90}\cdot 5^{45}$	$3$	$88.6243277641$			✓	$D_{45}:C_{12}$ (as 45T144)	not computed	$2$	$22$
45.1.450...544.1	x^45 + 4x - 4	$45$	[1,22]	$2^{44}\cdot 523\cdot 326083\cdot 86999456098802843\cdot 17\!\cdots\!07$	$5$	$88.6884233855$			?	$S_{45}$ (as 45T10923)	not computed	$2$	$22$
45.45.977...089.1	x^45 - x^44 - 72x^43 + 67x^42 + 2321x^41 - 2007x^40 - 44393x^39 + 35655x^38 + 562984x^37 - 420187x^36 - 5012298x^35 + 3480849x^34 + 32367724x^33 - 20955723x^32 - 154542085x^31 + 93497512x^30 + 551503498x^29 - 312562651x^28 - 1478859633x^27 + 786888918x^26 + 2984367290x^25 - 1493106677x^24 - 4527360022x^23 + 2130398676x^22 + 5146818792x^21 - 2274599139x^20 - 4361796744x^19 + 1804001386x^18 + 2733500368x^17 - 1051995625x^16 - 1251105602x^15 + 444673277x^14 + 410259354x^13 - 133494819x^12 - 93584992x^11 + 27616610x^10 + 14189768x^9 - 3755862x^8 - 1331682x^7 + 310282x^6 + 69020x^5 - 13468x^4 - 1660x^3 + 232x^2 + 16x - 1	$45$	[45,0]	$7^{30}\cdot 31^{42}$	$2$	$90.226949455$		✓	?	$C_3\times C_{15}$ (as 45T2)	trivial	$2$	$44$	$604682720155280400000000000000$
45.45.436...561.1	x^45 - x^44 - 76x^43 + 71x^42 + 2587x^41 - 2253x^40 - 52277x^39 + 42329x^38 + 700945x^37 - 526048x^36 - 6604336x^35 + 4578520x^34 + 45186997x^33 - 28840788x^32 - 228874394x^31 + 134081171x^30 + 867295136x^29 - 465239246x^28 - 2469432362x^27 + 1211308198x^26 + 5279515898x^25 - 2368332022x^24 - 8432662207x^23 + 3466272920x^22 + 9971146414x^21 - 3771201953x^20 - 8615444602x^19 + 3016692905x^18 + 5349176614x^17 - 1747589185x^16 - 2338480852x^15 + 719039461x^14 + 702585559x^13 - 204971923x^12 - 140848481x^11 + 39126498x^10 + 18138585x^9 - 4764404x^8 - 1426972x^7 + 345013x^6 + 64118x^5 - 13350x^4 - 1490x^3 + 225x^2 + 15x - 1	$45$	[45,0]	$11^{36}\cdot 19^{40}$	$2$	$93.279028795$		✓	?	$C_{45}$ (as 45T1)	trivial	$2$	$44$	$1164989215047236500000000000000$
45.45.940...689.1	x^45 - 81x^43 + 2943x^41 - 63576x^39 + 912699x^37 - 256x^36 - 9221688x^35 + 11619x^34 + 67767147x^33 - 228393x^32 - 369266337x^31 + 2577030x^30 + 1508018391x^29 - 18638901x^28 - 4636251652x^27 + 91308222x^26 + 10725370218x^25 - 311639850x^24 - 18578308230x^23 + 749536389x^22 + 23873708220x^21 - 1268865972x^20 - 22446274041x^19 + 1494154410x^18 + 15154469253x^17 - 1197712170x^16 - 7173383040x^15 + 633986568x^14 + 2312491545x^13 - 213869688x^12 - 490418469x^11 + 44511588x^10 + 65361426x^9 - 5507676x^8 - 5123475x^7 + 385695x^6 + 214380x^5 - 14391x^4 - 4176x^3 + 243x^2 + 27x - 1	$45$	[45,0]	$3^{110}\cdot 11^{36}$	$2$	$99.8643658547$		✓	?	$C_{45}$ (as 45T1)	trivial	$2$	$44$	$7652474177847196000000000000000$
45.45.183...361.1	x^45 - 87x^43 - 4x^42 + 3402x^41 + 300x^40 - 79106x^39 - 10008x^38 + 1219668x^37 + 196264x^36 - 13165542x^35 - 2519472x^34 + 102436164x^33 + 22316760x^32 - 583045167x^31 - 140145264x^30 + 2440735434x^29 + 631757436x^28 - 7504722910x^27 - 2050106328x^26 + 16845457116x^25 + 4771066968x^24 - 27354225744x^23 - 7899876240x^22 + 31819110888x^21 + 9218870784x^20 - 26289431304x^19 - 7517163552x^18 + 15324352272x^17 + 4245866400x^16 - 6258116631x^15 - 1643669037x^14 + 1770836592x^13 + 429144192x^12 - 340508538x^11 - 73586928x^10 + 43022076x^9 + 7934841x^8 - 3375522x^7 - 502012x^6 + 149688x^5 + 16758x^4 - 3200x^3 - 252x^2 + 24x + 1	$45$	[45,0]	$3^{60}\cdot 31^{42}$	$2$	$106.683990948$		✓	?	$C_3\times C_{15}$ (as 45T2)	not computed	$2$	$44$
45.45.295...689.1	x^45 - 3x^44 - 108x^43 + 296x^42 + 5217x^41 - 13005x^40 - 149828x^39 + 337863x^38 + 2868057x^37 - 5809689x^36 - 38881407x^35 + 70098207x^34 + 387120467x^33 - 613625013x^32 - 2896408122x^31 + 3972622452x^30 + 16519787829x^29 - 19205853294x^28 - 72406643558x^27 + 69489283683x^26 + 244599321027x^25 - 187254237300x^24 - 635787323022x^23 + 371102281773x^22 + 1263897395760x^21 - 528600088722x^20 - 1901669780781x^19 + 520023114157x^18 + 2134290033054x^17 - 327330093672x^16 - 1754567507744x^15 + 107410900356x^14 + 1034842778925x^13 + 1036802542x^12 - 428135520330x^11 - 14111627571x^10 + 121049080943x^9 + 4346148948x^8 - 22551409551x^7 - 290753084x^6 + 2597605155x^5 - 77625633x^4 - 161647682x^3 + 13050165x^2 + 3741168x - 437977	$45$	[45,0]	$3^{60}\cdot 7^{30}\cdot 11^{36}$	$3$	$107.813839968$		✓	?	$C_3\times C_{15}$ (as 45T2)	trivial	$2$	$44$	$36716059087827736000000000000000$
45.1.461...549.1	x^45 + x - 3	$45$	[1,22]	$41\cdot 281\cdot 2689\cdot 3061\cdot 9790127\cdot 49\!\cdots\!43$	$6$	$114.60665493$			?	$S_{45}$ (as 45T10923)	not computed	$2$	$22$
45.3.605...203.1	x^45 - 3x - 1	$45$	[3,21]	$-\,3^{45}\cdot 66012539\cdot 28278051239\cdot 68372307116461\cdot 16\!\cdots\!41$	$5$	$121.353626895$			✓	$S_{45}$ (as 45T10923)	not computed	$2$	$23$
45.1.605...453.1	x^45 + 3x - 1	$45$	[1,22]	$3^{45}\cdot 991\cdot 5482500513935539\cdot 37\!\cdots\!79$	$4$	$121.353626895$			✓	$S_{45}$ (as 45T10923)	not computed	$2$	$22$
45.1.605...328.1	x^45 + 3x - 2	$45$	[1,22]	$2^{44}\cdot 3^{45}\cdot 8431\cdot 40996793\cdot 141817543613\cdot 23\!\cdots\!89$	$6$	$121.353628837$			✓	$S_{45}$ (as 45T10923)	not computed	$2$	$22$
45.1.244...853.1	x^45 - 2x - 3	$45$	[1,22]	$1294351\cdot 15211842839\cdot 12\!\cdots\!77$	$3$	$131.744069354$			✓	$S_{45}$ (as 45T10923)	not computed	$2$	$22$
45.1.244...829.1	x^45 - x - 3	$45$	[1,22]	$394759\cdot 17295724778674525629079\cdot 35\!\cdots\!89$	$3$	$131.744069355$			✓	$S_{45}$ (as 45T10923)	not computed	$2$	$22$
45.1.244...125.1	x^45 - 3	$45$	[1,22]	$3^{134}\cdot 5^{45}$	$2$	$131.744069355$			✓	$D_{45}:C_{12}$ (as 45T144)	not computed	$2$	$22$
45.45.113...889.1	x^45 - 12x^44 - 38x^43 + 936x^42 - 488x^41 - 32994x^40 + 61155x^39 + 695151x^38 - 1826452x^37 - 9745559x^36 + 31398650x^35 + 95576968x^34 - 363031278x^33 - 668271620x^32 + 3006554151x^31 + 3299628259x^30 - 18405469866x^29 - 10819187452x^28 + 84606290574x^27 + 17798672756x^26 - 293624042239x^25 + 25779977473x^24 + 766879229695x^23 - 259704306954x^22 - 1488735953755x^21 + 843265985246x^20 + 2094958274346x^19 - 1672596038928x^18 - 2036992655261x^17 + 2211683013511x^16 + 1229593352332x^15 - 1960884055901x^14 - 305227614428x^13 + 1128154934100x^12 - 126915280282x^11 - 391023252143x^10 + 124192084723x^9 + 69369604379x^8 - 37452923715x^7 - 3334757683x^6 + 4610823573x^5 - 413774775x^4 - 188088413x^3 + 35065204x^2 - 872335x + 619	$45$	[45,0]	$13^{30}\cdot 31^{42}$	$2$	$136.322167425$		✓	?	$C_3\times C_{15}$ (as 45T2)	not computed	$2$	$44$
45.45.217...321.1	x^45 - x^44 - 88x^43 + 83x^42 + 3486x^41 - 3092x^40 - 82393x^39 + 68502x^38 + 1298642x^37 - 1008411x^36 - 14455343x^35 + 10441803x^34 + 117428375x^33 - 78557259x^32 - 709738502x^31 + 437535596x^30 + 3225742725x^29 - 1822257498x^28 - 11074210163x^27 + 5697019051x^26 + 28704796942x^25 - 13361047180x^24 - 55904143642x^23 + 23423035295x^22 + 81043444290x^21 - 30561670072x^20 - 86189587932x^19 + 29605929893x^18 + 65831554861x^17 - 21311114591x^16 - 35027996039x^15 + 11388975649x^14 + 12410963786x^13 - 4429059287x^12 - 2711901594x^11 + 1176564667x^10 + 302440276x^9 - 189664142x^8 - 3791931x^7 + 14878752x^6 - 2048263x^5 - 256726x^4 + 86268x^3 - 7415x^2 + 215x - 1	$45$	[45,0]	$181^{44}$	$1$	$161.253050772$		✓		$C_{45}$ (as 45T1)	trivial	$2$	$44$	$2805249427577283000000000000000000000$
45.3.253...304.1	x^45 - 4x - 2	$45$	[3,21]	$-\,2^{44}\cdot 2834789\cdot 50\!\cdots\!71$	$3$	$161.80483586$			✓	$S_{45}$ (as 45T10923)	not computed	$2$	$23$
45.1.253...429.1	x^45 + 4x - 1	$45$	[1,22]	$41\cdot 547\cdot 107899001480198069\cdot 10\!\cdots\!83$	$4$	$161.80483586$			✓	$S_{45}$ (as 45T10923)	not computed	$2$	$22$
45.1.253...304.1	x^45 + 4x - 2	$45$	[1,22]	$2^{44}\cdot 7\cdot 2687\cdot 76\!\cdots\!41$	$4$	$161.80483586$			✓	$S_{45}$ (as 45T10923)	not computed	$2$	$22$
45.45.165...961.1	x^45 - 4x^44 - 114x^43 + 468x^42 + 5696x^41 - 24132x^40 - 165566x^39 + 729869x^38 + 3130045x^37 - 14526130x^36 - 40702810x^35 + 202181480x^34 + 374739344x^33 - 2040701711x^32 - 2468141099x^31 + 15280860430x^30 + 11523689449x^29 - 86102308596x^28 - 36476021474x^27 + 368042106614x^26 + 66266177672x^25 - 1197228116258x^24 + 511532340x^23 + 2959992694385x^22 - 394556499523x^21 - 5529580093472x^20 + 1265687493078x^19 + 7719490702430x^18 - 2271295840968x^17 - 7914078560767x^16 + 2645087732416x^15 + 5804631677810x^14 - 2048306537737x^13 - 2929193071000x^12 + 1039444940408x^11 + 957147248584x^10 - 333732759991x^9 - 182597145321x^8 + 64595300484x^7 + 16257686900x^6 - 6916885901x^5 - 166352258x^4 + 298954277x^3 - 40977465x^2 + 2118031x - 36851	$45$	[45,0]	$11^{36}\cdot 37^{40}$	$2$	$168.682968895$		✓		$C_{45}$ (as 45T1)	trivial	$2$	$44$	$1875607941327826500000000000000000000$
45.1.191...432.1	x^45 - 2x - 4	$45$	[1,22]	$2^{86}\cdot 166289\cdot 17194056911\cdot 97370596099401809\cdot 89\!\cdots\!83$	$5$	$169.244390536$			?	$S_{45}$ (as 45T10923)	not computed	$2$	$22$
45.1.191...568.1	x^45 + 2x - 4	$45$	[1,22]	$2^{86}\cdot 59\cdot 42\!\cdots\!43$	$3$	$169.244390536$			?	$S_{45}$ (as 45T10923)	not computed	$2$	$22$
45.45.217...129.1	x^45 - 12x^44 - 50x^43 + 1120x^42 - 626x^41 - 44264x^40 + 106520x^39 + 966733x^38 - 3644562x^37 - 12564205x^36 + 68449875x^35 + 92270622x^34 - 830216501x^33 - 202049055x^32 + 6933616229x^31 - 3181542881x^30 - 41084005259x^29 + 40234212427x^28 + 174510130968x^27 - 250382990469x^26 - 527354195438x^25 + 1015613064703x^24 + 1094857977723x^23 - 2871848912941x^22 - 1403630755463x^21 + 5763542313829x^20 + 629825101852x^19 - 8167242308412x^18 + 1257688359124x^17 + 7983130477206x^16 - 2778691581109x^15 - 5144196139934x^14 + 2589633668016x^13 + 2011525458240x^12 - 1316532612469x^11 - 396963769511x^10 + 358975449036x^9 + 14178066293x^8 - 45168898819x^7 + 5258463166x^6 + 1537215457x^5 - 288043322x^4 - 5291206x^3 + 2457345x^2 - 9309x - 6089	$45$	[45,0]	$7^{30}\cdot 61^{42}$	$2$	$169.709650609$		✓	?	$C_3\times C_{15}$ (as 45T2)	not computed	$2$	$44$
45.1.767...672.1	x^45 - 3x - 4	$45$	[1,22]	$2^{89}\cdot 3^{45}\cdot 61\cdot 1183211\cdot 1595562959\cdot 36\!\cdots\!03$	$6$	$174.53936573$			✓	$S_{45}$ (as 45T10923)	not computed	$2$	$22$
45.45.999...561.1	x^45 - 12x^44 - 68x^43 + 1390x^42 - 278x^41 - 68270x^40 + 176199x^39 + 1808389x^38 - 8154574x^37 - 26005805x^36 + 196321268x^35 + 127187382x^34 - 2913805970x^33 + 2272631340x^32 + 27669670927x^31 - 52510157887x^30 - 162002621792x^29 + 526806359978x^28 + 468745083598x^27 - 3175101889498x^26 + 532391340063x^25 + 12135569776697x^24 - 10651958891479x^23 - 28871893561060x^22 + 45196495080913x^21 + 38272655903792x^20 - 105664143365844x^19 - 13349385343870x^18 + 153132315545987x^17 - 41028745873427x^16 - 141811047613612x^15 + 76543731297893x^14 + 83515595010770x^13 - 65499266094722x^12 - 29808531214812x^11 + 32918818373161x^10 + 5404646072895x^9 - 10084991417837x^8 - 16286468525x^7 + 1821205338619x^6 - 180698614131x^5 - 173451418339x^4 + 28592722199x^3 + 6396948952x^2 - 1303357845x - 3078919	$45$	[45,0]	$19^{30}\cdot 31^{42}$	$2$	$175.565824969$		✓	?	$C_3\times C_{15}$ (as 45T2)	not computed	$2$	$44$
45.45.299...625.1	x^45 - 5x^44 - 120x^43 + 570x^42 + 6560x^41 - 29130x^40 - 216795x^39 + 884935x^38 + 4846835x^37 - 17873115x^36 - 77748559x^35 + 254358990x^34 + 926664900x^33 - 2637505030x^32 - 8389061335x^31 + 20318079721x^30 + 58494148730x^29 - 117428976980x^28 - 316667682495x^27 + 510052425895x^26 + 1335050206763x^25 - 1653394093375x^24 - 4375338382740x^23 + 3923851568060x^22 + 11069977015865x^21 - 6532787291841x^20 - 21348397264600x^19 + 6845293868685x^18 + 30760204370920x^17 - 2712180162090x^16 - 32145143355065x^15 - 3532224571660x^14 + 23314933370325x^13 + 6500465979650x^12 - 10976198292280x^11 - 4703287953351x^10 + 3011509345140x^9 + 1752830160915x^8 - 400149323895x^7 - 327698710405x^6 + 19849150584x^5 + 30510229725x^4 + 7497705x^3 - 1362119415x^2 - 14453695x + 22808701	$45$	[45,0]	$5^{72}\cdot 19^{40}$	$2$	$179.896152255$		✓	?	$C_{45}$ (as 45T1)	trivial	$2$	$44$	$4022487388915899600000000000000000000$
45.3.118...000.1	x^45 - 5x - 2	$45$	[3,21]	$-\,2^{44}\cdot 5^{45}\cdot 73\cdot 44175746519\cdot 6490952564449\cdot 14705222713099\cdot 7728853529686445339$	$7$	$185.499010511$			?	$S_{45}$ (as 45T10923)	not computed	$2$	$23$
45.3.233...875.1	x^45 - 5x - 3	$45$	[3,21]	$-\,5^{43}\cdot 157\cdot 1531\cdot 4729\cdot 4801\cdot 15817\cdot 31873\cdot 97849\cdot 18359951437\cdot 35107655355337\cdot 11818574496687068323309$	$11$	$188.293867872$			?	$S_{45}$ (as 45T10923)	not computed	$2$	$23$
45.45.644...625.1	x^45 - 135x^43 - 45x^42 + 8145x^41 + 5076x^40 - 290700x^39 - 253620x^38 + 6857235x^37 + 7452610x^36 - 113268978x^35 - 144333495x^34 + 1355213265x^33 + 1957216455x^32 - 11983335705x^31 - 19266777171x^30 + 79141746870x^29 + 140783463765x^28 - 391240008255x^27 - 773615354895x^26 + 1437267934764x^25 + 3215872493700x^24 - 3839971488165x^23 - 10109340177300x^22 + 7085017431465x^21 + 23873005106874x^20 - 7751347674075x^19 - 41764000577760x^18 + 1270029598110x^17 + 52868417349600x^16 + 10969424061639x^15 - 46623586775670x^14 - 19170786833010x^13 + 26882974463550x^12 + 16378966497285x^11 - 8981328155022x^10 - 7825331392520x^9 + 1236586926825x^8 + 1998991148400x^7 + 84870189090x^6 - 236319447555x^5 - 31508573040x^4 + 10090496085x^3 + 1414058625x^2 - 109748520x - 10224199	$45$	[45,0]	$3^{110}\cdot 5^{72}$	$2$	$192.596507455$		✓	?	$C_{45}$ (as 45T1)	not computed	$2$	$44$
45.1.145...000.1	x^45 + 5x - 2	$45$	[1,22]	$2^{42}\cdot 5^{46}\cdot 53\cdot 22846124160878734429091761\cdot 19\!\cdots\!97$	$5$	$196.120232448$				$S_{45}$ (as 45T10923)	not computed	$2$	$22$
45.45.408...321.1	x^45 - 3x^44 - 126x^43 + 350x^42 + 7095x^41 - 18207x^40 - 237254x^39 + 560949x^38 + 5280957x^37 - 11465163x^36 - 83127609x^35 + 164960568x^34 + 959694733x^33 - 1729668720x^32 - 8316855543x^31 + 13495839126x^30 + 54911329452x^29 - 79318322604x^28 - 278624618803x^27 + 353264598507x^26 + 1090386630918x^25 - 1193881051406x^24 - 3286918329246x^23 + 3054422504946x^22 + 7584376524784x^21 - 5885779838802x^20 - 13239515051214x^19 + 8489225140885x^18 + 17170281215082x^17 - 9118144480932x^16 - 16115327765898x^15 + 7281918623109x^14 + 10535410010724x^13 - 4323241543716x^12 - 4518883017183x^11 + 1877328461526x^10 + 1138556965481x^9 - 554295751305x^8 - 124509763362x^7 + 91825606123x^6 - 3656082528x^5 - 5240896776x^4 + 961503906x^3 - 1541688x^2 - 11847522x + 756289	$45$	[45,0]	$3^{60}\cdot 61^{42}$	$2$	$200.66402487$		✓	?	$C_3\times C_{15}$ (as 45T2)	not computed	$2$	$44$
45.3.582...875.1	x^45 - 5x - 1	$45$	[3,21]	$-\,5^{45}\cdot 13\cdot 47\cdot 241\cdot 313\cdot 10159\cdot 1560681193\cdot 441481146991\cdot 24561359840613046207\cdot 258812619101427272051$	$10$	$202.256044825$			✓	$S_{45}$ (as 45T10923)	not computed	$2$	$23$
45.1.582...125.1	x^45 + 5x - 1	$45$	[1,22]	$5^{46}\cdot 101\cdot 677\cdot 119549\cdot 842977\cdot 818961053\cdot 72\!\cdots\!73$	$7$	$202.256044825$			✓	$S_{45}$ (as 45T10923)	not computed	$2$	$22$
45.1.582...125.1	x^45 + 5x - 3	$45$	[1,22]	$5^{46}\cdot 29\cdot 699023939659537\cdot 20\!\cdots\!01$	$4$	$202.256044843$			✓	$S_{45}$ (as 45T10923)	not computed	$2$	$22$
45.1.583...000.1	x^45 + 5x - 4	$45$	[1,22]	$2^{89}\cdot 5^{46}\cdot 149\cdot 44\!\cdots\!01$	$4$	$202.261961044$			✓	$S_{45}$ (as 45T10923)	not computed	$2$	$22$
45.45.202...625.1	x^45 - 165x^43 - 25x^42 + 12060x^41 + 3486x^40 - 519330x^39 - 214140x^38 + 14776560x^37 + 7718745x^36 - 295077669x^35 - 182852610x^34 + 4284179615x^33 + 3016157820x^32 - 46197393465x^31 - 35772719505x^30 + 374607222195x^29 + 310484223975x^28 - 2298730688540x^27 - 1988244775980x^26 + 10695933805596x^25 + 9407317026635x^24 - 37696094037390x^23 - 32764647222885x^22 + 100289481110340x^21 + 83332538318277x^20 - 200279250507195x^19 - 152889355168310x^18 + 297466429398705x^17 + 198745289480940x^16 - 323624520119411x^15 - 178210655500665x^14 + 251547979741875x^13 + 105785393431525x^12 - 134218212107550x^11 - 38927292179565x^10 + 46104688292390x^9 + 7956837983055x^8 - 9173261413650x^7 - 765305596255x^6 + 891053703312x^5 + 40709257785x^4 - 38148076985x^3 - 1973427960x^2 + 606052050x + 47691757	$45$	[45,0]	$3^{60}\cdot 5^{72}\cdot 7^{30}$	$3$	$207.927711304$		✓	?	$C_3\times C_{15}$ (as 45T2)	not computed	$2$	$44$
45.45.690...281.1	x^45 - 4x^44 - 146x^43 + 698x^42 + 8985x^41 - 51888x^40 - 296427x^39 + 2177976x^38 + 5305247x^37 - 57476954x^36 - 34012820x^35 + 1002110429x^34 - 626632964x^33 - 11753633659x^32 + 18688879395x^31 + 91599636078x^30 - 237738671647x^29 - 440115277508x^28 + 1861290436646x^27 + 876346054868x^26 - 9636797401413x^25 + 3638557275086x^24 + 33031864898329x^23 - 35155604700368x^22 - 70196515943930x^21 + 133850962002890x^20 + 68063148815178x^19 - 296060971462243x^18 + 63115875057640x^17 + 386991855136149x^16 - 292070548579474x^15 - 252378957195025x^14 + 393110942284862x^13 - 3989425272418x^12 - 248373295675609x^11 + 116468486134606x^10 + 55635812822046x^9 - 63558461838326x^8 + 10039317831256x^7 + 9501878099079x^6 - 4834005607020x^5 + 527330092663x^4 + 166660835109x^3 - 51025747438x^2 + 4407259697x - 98524081	$45$	[45,0]	$19^{40}\cdot 31^{36}$	$2$	$213.677710939$		✓		$C_{45}$ (as 45T1)	trivial	$2$	$44$	$560427797213053600000000000000000000000$
45.1.141...125.1	x^45 - 5	$45$	[1,22]	$3^{90}\cdot 5^{89}$	$2$	$217.095015089$			✓	$D_{45}:C_{12}$ (as 45T144)	not computed	$2$	$22$
45.45.148...969.1	x^45 - 9x^44 - 117x^43 + 1356x^42 + 4455x^41 - 86382x^40 + 4596x^39 + 3024342x^38 - 5886234x^37 - 62776190x^36 + 223064037x^35 + 751420521x^34 - 4412144961x^33 - 3725440704x^32 + 54057041307x^31 - 28786222110x^30 - 426126343077x^29 + 673008341841x^28 + 2086637912508x^27 - 5873721786378x^26 - 5053254569676x^25 + 30385493847345x^24 - 5904503198856x^23 - 98922911866245x^22 + 93605350409913x^21 + 191046717571311x^20 - 349809055484526x^19 - 147155959283342x^18 + 707251464652203x^17 - 217826629489476x^16 - 797405893685064x^15 + 705978096992721x^14 + 378713501361567x^13 - 782478874269585x^12 + 139525392055671x^11 + 385252617992454x^10 - 250562776470715x^9 - 36607492213488x^8 + 95351499735039x^7 - 31186566059442x^6 - 5609742817023x^5 + 6576945066567x^4 - 1857401457582x^3 + 224711418717x^2 - 8430571116x - 155181097	$45$	[45,0]	$3^{110}\cdot 31^{36}$	$2$	$228.762985377$		✓	?	$C_{45}$ (as 45T1)	not computed	$2$	$44$
45.45.112...281.1	x^45 - x^44 - 132x^43 + 301x^42 + 7581x^41 - 27065x^40 - 236809x^39 + 1229173x^38 + 3960874x^37 - 33065607x^36 - 18797995x^35 + 555716542x^34 - 619527603x^33 - 5732299123x^32 + 15235581842x^31 + 30609318626x^30 - 168897578817x^29 + 17112929652x^28 + 1054352970448x^27 - 1501837759883x^26 - 3320354588485x^25 + 10782132568732x^24 - 107051646226x^23 - 36936809485370x^22 + 41830258905956x^21 + 53083505529011x^20 - 152445251342987x^19 + 42842896041923x^18 + 229594603485553x^17 - 272222797945867x^16 - 70739760279828x^15 + 364126674087072x^14 - 209159107972130x^13 - 142016333800362x^12 + 231101895832035x^11 - 63870399263881x^10 - 62082302112786x^9 + 49149720219336x^8 - 3670701881262x^7 - 8040338248733x^6 + 2565873490427x^5 + 306896523050x^4 - 230447557112x^3 + 11171763392x^2 + 5932497375x - 637239997	$45$	[45,0]	$271^{44}$	$1$	$239.278295664$		✓		$C_{45}$ (as 45T1)	not computed	$2$	$44$
45.45.252...929.1	x^45 - 12x^44 - 80x^43 + 1424x^42 + 1516x^41 - 74554x^40 + 63158x^39 + 2282501x^38 - 4255902x^37 - 45636421x^36 + 116693559x^35 + 630121996x^34 - 1971613347x^33 - 6193698077x^32 + 22855343401x^31 + 44007670585x^30 - 190617019593x^29 - 226920195907x^28 + 1172746429282x^27 + 842990049201x^26 - 5394671280584x^25 - 2206384597765x^24 + 18666651459717x^23 + 3871477687999x^22 - 48596558981735x^21 - 4036750693451x^20 + 94693820108958x^19 + 1546861746446x^18 - 136570614884744x^17 + 956863921562x^16 + 143064103358001x^15 + 102341290612x^14 - 105649963477592x^13 - 2816833651750x^12 + 52484763220205x^11 + 2919265367283x^10 - 16311452643376x^9 - 1104335997267x^8 + 2857645920655x^7 + 105919440856x^6 - 255094574859x^5 + 8466426668x^4 + 8654209646x^3 - 1026667213x^2 + 14388119x + 1507921	$45$	[45,0]	$13^{30}\cdot 61^{42}$	$2$	$256.411056161$		✓	?	$C_3\times C_{15}$ (as 45T2)	not computed	$2$	$44$
45.45.162...641.1	x^45 - 4x^44 - 182x^43 + 580x^42 + 15229x^41 - 35784x^40 - 771497x^39 + 1192202x^38 + 26249095x^37 - 21282586x^36 - 630350986x^35 + 101314575x^34 + 10957230656x^33 + 4486413137x^32 - 139417559409x^31 - 128053969474x^30 + 1299055132435x^29 + 1816090021004x^28 - 8766783201604x^27 - 16658946907076x^26 + 41634175647095x^25 + 105419181053468x^24 - 129801264303153x^23 - 468263377533416x^22 + 210417608171782x^21 + 1454214352745320x^20 + 113648989333176x^19 - 3097196961798623x^18 - 1450605309591570x^17 + 4363534978783893x^16 + 3500531720706214x^15 - 3807203164617687x^14 - 4497701352355764x^13 + 1760587964112158x^12 + 3382378542501223x^11 - 165688879950870x^10 - 1480388191573288x^9 - 205996027224400x^8 + 358811476146228x^7 + 88160595048203x^6 - 42989403930482x^5 - 13014696239433x^4 + 1879419740489x^3 + 646702182070x^2 + 19352782133x - 2280393187	$45$	[45,0]	$19^{40}\cdot 41^{36}$	$2$	$267.2372247$		✓	?	$C_{45}$ (as 45T1)	not computed	$2$	$44$
45.45.105...761.1	x^45 - 4x^44 - 194x^43 + 836x^42 + 16500x^41 - 76882x^40 - 811248x^39 + 4130184x^38 + 25559474x^37 - 145049280x^36 - 538597921x^35 + 3530594867x^34 + 7615564821x^33 - 61610572814x^32 - 68317895227x^31 + 786429242050x^30 + 287086043611x^29 - 7425134094508x^28 + 1391788361320x^27 + 52087220030130x^26 - 32183862662002x^25 - 271116028008606x^24 + 264064430436474x^23 + 1039304723755570x^22 - 1345885450620938x^21 - 2889398096911074x^20 + 4691240971935913x^19 + 5661912712400497x^18 - 11481658937434788x^17 - 7388527635358822x^16 + 19748315799639590x^15 + 5543796759733632x^14 - 23515522924776395x^13 - 895060410571712x^12 + 18817979236586386x^11 - 2391413888018270x^10 - 9652129249107031x^9 + 2328285637187904x^8 + 2951322314183680x^7 - 960094366581828x^6 - 477351520888160x^5 + 190413802657905x^4 + 31093339218140x^3 - 15654659537914x^2 - 188842256201x + 306884845321	$45$	[45,0]	$11^{36}\cdot 73^{40}$	$2$	$308.603704387$		✓	?	$C_{45}$ (as 45T1)	not computed	$2$	$44$
45.45.235...625.1	x^45 - 15x^44 - 90x^43 + 2245x^42 + 840x^41 - 149682x^40 + 233625x^39 + 5893830x^38 - 15309120x^37 - 153159405x^36 + 505833687x^35 + 2780167860x^34 - 10777640365x^33 - 36390969195x^32 + 160894854450x^31 + 349558305696x^30 - 1751940770010x^29 - 2483116182570x^28 + 14226276458010x^27 + 13037929556940x^26 - 87229174471284x^25 - 50137706272620x^24 + 406336593221610x^23 + 138267603359730x^22 - 1439822630956295x^21 - 262195938148443x^20 + 3868718864967360x^19 + 311910060390275x^18 - 7821266721741750x^17 - 175081417856730x^16 + 11738415157749574x^15 - 32411856380685x^14 - 12806776910595090x^13 + 44301971232950x^12 + 9836514943009755x^11 + 117791800035840x^10 - 5063789878500180x^9 - 176503490451285x^8 + 1618208036238660x^7 + 90536277582715x^6 - 283553373081756x^5 - 18640864878495x^4 + 21751317924475x^3 + 974579665770x^2 - 434206226325x + 15265738099	$45$	[45,0]	$3^{60}\cdot 5^{72}\cdot 13^{30}$	$3$	$314.153991064$		✓	?	$C_3\times C_{15}$ (as 45T2)	not computed	$2$	$44$