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Label Polynomial Discriminant Galois group Class group
35.1.109...339.1 x35 - x - 1 \( -\,19\cdot 43350623\cdot 10394177419177\cdot 127405006561314526913842526847311 \) $S_{35}$ (as 35T407) trivial (GRH)
35.1.403...123.1 x35 + 2x - 1 \( -\,256048319\cdot 1577651591526453474215509975271306082814925125043973317 \) $S_{35}$ (as 35T407) trivial (GRH)
35.35.876...281.1 x35 - x34 - 34x33 + 33x32 + 528x31 - 496x30 - 4960x29 + 4495x28 + 31465x27 - 27405x26 - 142506x25 + 118755x24 + 475020x23 - 376740x22 - 1184040x21 + 888030x20 + 2220075x19 - 1562275x18 - 3124550x17 + 2042975x16 + 3268760x15 - 1961256x14 - 2496144x13 + 1352078x12 + 1352078x11 - 646646x10 - 497420x9 + 203490x8 + 116280x7 - 38760x6 - 15504x5 + 3876x4 + 969x3 - 153x2 - 18x + 1 \( 71^{34} \) $C_{35}$ (as 35T1) trivial (GRH)
35.1.219...944.1 x35 + 4x - 4 \( -\,2^{34}\cdot 3\cdot 227\cdot 499\cdot 1637\cdot 252983\cdot 13122193474139\cdot 69164815108090306157070281 \) $S_{35}$ (as 35T407) n/a
35.1.181...504.1 x35 - 4x - 4 \( -\,2^{34}\cdot 2393\cdot 3027347\cdot 3480929\cdot 23465153\cdot 86816318477729\cdot 20545919111781857 \) $S_{35}$ (as 35T407) trivial (GRH)
35.1.185...752.1 x35 - 2x - 2 \( -\,2^{34}\cdot 3\cdot 101\cdot 181\cdot 20265277861\cdot 970834838597032055518467053783192081261 \) $S_{35}$ (as 35T407) trivial (GRH)
35.1.189...464.1 x35 - x - 2 \( -\,2^{35}\cdot 23\cdot 29\cdot 5408561\cdot 3295715551039421859593\cdot 46365427582714972609103 \) $S_{35}$ (as 35T407) trivial (GRH)
35.1.189...671.1 x35 - x - 4 \( -\,21529\cdot 108949\cdot 6512477\cdot 1233879787294159\cdot 1004928692423983036960429614171257 \) $S_{35}$ (as 35T407) trivial (GRH)
35.1.189...000.1 x35 - 2 \( -\,2^{34}\cdot 5^{35}\cdot 7^{35} \) 35T20 n/a
35.1.193...248.1 x35 + 2x - 2 \( -\,2^{34}\cdot 1126020777164885927974614534416129059276178480254685947 \) $S_{35}$ (as 35T407) n/a
35.3.588...077.1 x35 - 3x - 1 \( 263\cdot 2236512584055526076013600529526179910354990193614694867151817964179 \) $S_{35}$ (as 35T407) n/a
35.1.588...827.1 x35 + 3x - 1 \( -\,11\cdot 98621\cdot 1256737\cdot 431440197517624808800874835977068316565768413760949105541 \) $S_{35}$ (as 35T407) n/a
35.1.588...952.1 x35 + 3x - 2 \( -\,2^{35}\cdot 67\cdot 997\cdot 10501\cdot 21885937\cdot 61024809499\cdot 18273386263227299987114447833747 \) $S_{35}$ (as 35T407) n/a
35.1.165...904.1 x35 + 4x - 2 \( -\,2^{34}\cdot 3\cdot 291647\cdot 188120963917\cdot 64268062741853\cdot 129806582432617\cdot 699615044068223 \) $S_{35}$ (as 35T407) n/a
35.1.177...923.1 x35 - 3x - 3 \( -\,3^{34}\cdot 953\cdot 6256153603608033049\cdot 179003204879700031928572902324811 \) $S_{35}$ (as 35T407) n/a
35.1.183...339.1 x35 - x - 3 \( -\,31\cdot 593119931999166460046200152594306898166239148737980005862972411624269 \) $S_{35}$ (as 35T407) n/a
35.1.183...875.1 x35 - 3 \( -\,3^{34}\cdot 5^{35}\cdot 7^{35} \) 35T20 n/a
35.1.189...827.1 x35 + 3x - 3 \( -\,3^{34}\cdot 13\cdot 241667\cdot 21805563631\cdot 7788124267751\cdot 2132536222168538736270533 \) $S_{35}$ (as 35T407) n/a
35.35.107...681.1 x35 - 2x34 - 91x33 + 186x32 + 3529x31 - 7282x30 - 77406x29 + 160015x28 + 1074054x27 - 2215841x26 - 9975621x25 + 20528466x24 + 63908089x23 - 131541229x22 - 286306729x21 + 593348019x20 + 897545333x19 - 1896502635x18 - 1942677455x17 + 4283320775x16 + 2804705170x15 - 6752081061x14 - 2493142459x13 + 7254188151x12 + 1058706744x11 - 5105442290x10 + 147588576x9 + 2206890342x8 - 365733379x7 - 523140235x6 + 145322301x5 + 51716162x4 - 20476030x3 - 56585x2 + 426253x - 7523 \( 11^{28}\cdot 29^{30} \) $C_{35}$ (as 35T1) trivial (GRH)
35.3.138...264.1 x35 - 4x - 2 \( 2^{34}\cdot 19\cdot 168467557\cdot 252402204484836965139552299030470450770513914143787387 \) $S_{35}$ (as 35T407) n/a
35.3.138...389.1 x35 - 4x - 1 \( 13\cdot 7589\cdot 20542855181\cdot 1539824338977817412998292597\cdot 4447571988100751615228352051061 \) $S_{35}$ (as 35T407) n/a
35.1.138...139.1 x35 + 4x - 1 \( -\,3\cdot 11\cdot 313\cdot 2039\cdot 7735841\cdot 2351499104023\cdot 659569685611056889\cdot 54928069223700611994891513947 \) $S_{35}$ (as 35T407) n/a
35.1.138...139.1 x35 + 4x - 3 \( -\,9138888871558869679\cdot 1520773071289113273336033518817821571533849586015139741 \) $S_{35}$ (as 35T407) n/a
35.1.813...688.1 x35 - 2x - 4 \( -\,2^{66}\cdot 3\cdot 19661\cdot 769973\cdot 4451823287\cdot 5453072616450015712452596887160149 \) $S_{35}$ (as 35T407) n/a
35.1.813...312.1 x35 + 2x - 4 \( -\,2^{66}\cdot 53\cdot 73\cdot 4799\cdot 29426707\cdot 2986177911580117\cdot 675732378059188256648497 \) $S_{35}$ (as 35T407) n/a
35.1.325...048.1 x35 - 3x - 4 \( -\,2^{34}\cdot 1549\cdot 423786696769\cdot 86327107557848503\cdot 334237129377476731946563571596079 \) $S_{35}$ (as 35T407) n/a
35.1.325...536.1 x35 + x - 4 \( -\,2^{34}\cdot 3\cdot 13\cdot 485664990084185617541963221117971430129078178121023737305397111 \) $S_{35}$ (as 35T407) n/a
35.1.136...875.1 x35 + 5x - 3 \( -\,5^{33}\cdot 1098074000209\cdot 10706605584650121566295636839261553663967 \) $S_{35}$ (as 35T407) n/a
35.1.855...000.1 x35 + 5x - 2 \( -\,2^{35}\cdot 5^{35}\cdot 29\cdot 37\cdot 4783\cdot 451109\cdot 36948068942212518669550297789 \) $S_{35}$ (as 35T407) n/a
35.3.342...125.1 x35 - 5x - 3 \( 5^{35}\cdot 47\cdot 2551\cdot 98056103052957570805338836406495840027884930777 \) $S_{35}$ (as 35T407) n/a
35.3.342...000.1 x35 - 5x - 2 \( 2^{35}\cdot 3\cdot 5^{35}\cdot 846499\cdot 134736613369772875367972684185898269 \) $S_{35}$ (as 35T407) n/a
35.3.342...125.1 x35 - 5x - 1 \( 3\cdot 5^{35}\cdot 10273\cdot 14843\cdot 25700581463661603040632563709900234916117529 \) $S_{35}$ (as 35T407) n/a
35.1.342...875.1 x35 + 5x - 1 \( -\,5^{35}\cdot 11\cdot 241663\cdot 1377785519387\cdot 12423383848143479\cdot 258379951197664711 \) $S_{35}$ (as 35T407) n/a
35.1.345...000.1 x35 + 5x - 4 \( -\,2^{34}\cdot 5^{35}\cdot 23\cdot 30036282889711004677089205571002899788167 \) $S_{35}$ (as 35T407) n/a
35.1.675...875.1 x35 - 5x - 5 \( -\,5^{35}\cdot 29\cdot 2243199001\cdot 214847929968602317\cdot 1659496377096759652722647 \) $S_{35}$ (as 35T407) n/a
35.1.641...339.1 x35 - x - 5 \( -\,137320571\cdot 4673326232889111258230946275268277691256735317870963127470997996093209 \) $S_{35}$ (as 35T407) n/a
35.1.641...875.1 x35 - 5 \( -\,5^{69}\cdot 7^{35} \) 35T20 n/a
35.1.641...411.1 x35 + x - 5 \( -\,3\cdot 29\cdot 83\cdot 14920870913449\cdot 5956212470733679448044090102244808708234433700708917011580159 \) $S_{35}$ (as 35T407) n/a
35.1.641...827.1 x35 + 3x - 5 \( -\,47\cdot 397\cdot 1877\cdot 119039\cdot 441804439\cdot 348409282976275989473259857871463942961658812748071188309 \) $S_{35}$ (as 35T407) n/a
35.1.675...875.1 x35 + 5x - 5 \( -\,5^{35}\cdot 1481\cdot 13004394089\cdot 2075469389711\cdot 5810445451732846110092217889 \) $S_{35}$ (as 35T407) n/a
35.35.145...169.1 x35 - 2x34 - 121x33 + 124x32 + 6435x31 - 1020x30 - 195036x29 - 112597x28 + 3683986x27 + 4452851x26 - 44769607x25 - 80359740x24 + 347984933x23 + 850835561x22 - 1630509423x21 - 5621246939x20 + 3615565971x19 + 23234081997x18 + 3088781711x17 - 57619940147x16 - 39347873390x15 + 76695393961x14 + 92864249975x13 - 38675667681x12 - 94158719636x11 - 10380297650x10 + 42855721796x9 + 16263455858x8 - 7226936109x7 - 4634581071x6 - 47622511x5 + 349101928x4 + 70736582x3 + 5060011x2 + 136327x + 859 \( 11^{28}\cdot 43^{30} \) $C_{35}$ (as 35T1) trivial (GRH)
35.35.106...241.1 x35 - x34 - 102x33 + 231x32 + 4336x31 - 15350x30 - 93149x29 + 492148x28 + 885684x27 - 8797227x26 + 2494886x25 + 89830596x24 - 154446290x23 - 471756827x22 + 1664362308x21 + 444168124x20 - 8565464505x19 + 8653560326x18 + 19862461891x17 - 47903559470x16 + 736744022x15 + 100720726682x14 - 96083394992x13 - 62920019542x12 + 165504701751x11 - 60624002242x10 - 87564669300x9 + 86642725878x8 - 451900172x7 - 32473918206x6 + 11871839347x5 + 3432884529x4 - 2696920777x3 + 146105313x2 + 172726939x - 27756643 \( 211^{34} \) $C_{35}$ (as 35T1) trivial (GRH)
35.35.732...081.1 x35 - 7x34 - 112x33 + 742x32 + 5845x31 - 34447x30 - 188041x29 + 918544x28 + 4120599x27 - 15488536x26 - 63930916x25 + 170889838x24 + 709660070x23 - 1224719069x22 - 5607885533x21 + 5331715046x20 + 31035849173x19 - 10542390278x18 - 116936498434x17 - 15812866636x16 + 286852619543x15 + 146466192098x14 - 426702558436x13 - 357822103121x12 + 338413935629x11 + 421000631443x10 - 94811511375x9 - 240823440823x8 - 25297046987x7 + 58988457696x6 + 13678049308x5 - 6371815744x4 - 1687698845x3 + 280068103x2 + 55092156x - 2660503 \( 7^{60}\cdot 11^{28} \) $C_{35}$ (as 35T1) trivial (GRH)
35.35.103...625.1 x35 - 5x34 - 120x33 + 560x32 + 6265x31 - 27063x30 - 188895x29 + 746800x28 + 3677845x27 - 13130310x26 - 48923530x25 + 155517810x24 + 458129250x23 - 1279983515x22 - 3063191465x21 + 7446901792x20 + 14674072475x19 - 30859715040x18 - 50096318770x17 + 91037787910x16 + 120155286235x15 - 189447334860x14 - 197298653000x13 + 272612081065x12 + 212356717105x11 - 261877354307x10 - 139209319745x9 + 158110983885x8 + 48766657725x7 - 53789658890x6 - 7150843552x5 + 8233276160x4 + 456884545x3 - 363355535x2 - 50594420x - 1782107 \( 5^{56}\cdot 29^{30} \) $C_{35}$ (as 35T1) trivial (GRH)
35.35.180...921.1 x35 - x34 - 136x33 + 115x32 + 7922x31 - 5864x30 - 262379x29 + 176786x28 + 5536174x27 - 3463751x26 - 78912031x25 + 45605901x24 + 785104244x23 - 406720184x22 - 5548252572x21 + 2436396552x20 + 28031325744x19 - 9529852980x18 - 100888672963x17 + 22693210859x16 + 254967397769x15 - 26498170926x14 - 440501997963x13 - 3333796454x12 + 500538383949x11 + 44640325883x10 - 358942724140x9 - 43476115800x8 + 159203701176x7 + 16418359222x6 - 42718375268x5 - 1999390430x4 + 6413147106x3 - 204719982x2 - 415325205x + 48529823 \( 281^{34} \) $C_{35}$ (as 35T1) trivial (GRH)
35.35.497...681.1 x35 - 2x34 - 181x33 + 470x32 + 14259x31 - 45478x30 - 638530x29 + 2447153x28 + 17767052x27 - 82345759x26 - 312539633x25 + 1833247298x24 + 3264215879x23 - 27715265019x22 - 13487454777x21 + 286033632049x20 - 123264134993x19 - 1983204888009x18 + 2337315606897x17 + 8777927035267x16 - 17238219604018x15 - 21289728738165x14 + 71563023595709x13 + 8692436762607x12 - 169783075654432x11 + 94786315419610x10 + 202072200901306x9 - 240242794434974x8 - 58566297948415x7 + 212040077699383x6 - 73316281317651x5 - 51014137537536x4 + 37974482870362x3 - 1868368126575x2 - 3872034006535x + 804494744591 \( 11^{28}\cdot 71^{30} \) $C_{35}$ (as 35T1) trivial (GRH)
35.35.426...641.1 x35 - 2x34 - 147x33 + 384x32 + 8999x31 - 28384x30 - 300934x29 + 1116603x28 + 6027458x27 - 26518095x26 - 73782007x25 + 404019590x24 + 521840181x23 - 4069268247x22 - 1503940067x21 + 27441438677x20 - 6471979421x19 - 124171354119x18 + 81524582969x17 + 375114725905x16 - 364687984188x15 - 747339096335x14 + 926308497451x13 + 961292881275x12 - 1451786049968x11 - 771321612374x10 + 1427632011474x9 + 365928432486x8 - 868346663001x7 - 97103750919x6 + 312022190475x5 + 17703737306x4 - 59996070990x3 - 4579250401x2 + 4824514261x + 750695467 \( 29^{30}\cdot 31^{28} \) $C_{35}$ (as 35T1) trivial (GRH)
35.35.168...681.1 x35 - x34 - 204x33 + 437x32 + 17534x31 - 54290x30 - 824862x29 + 3275941x28 + 23317913x27 - 115242097x26 - 407103864x25 + 2577740505x24 + 4218284220x23 - 38412158946x22 - 19912715245x21 + 391393011501x20 - 73963916883x19 - 2766871309456x18 + 1816877075105x17 + 13678303310453x16 - 13286645514747x15 - 47446655533795x14 + 55834172665771x13 + 115251505419203x12 - 148585020568878x11 - 193921735357495x10 + 253198008831294x9 + 219700193289987x8 - 266521489745621x7 - 156623228737724x6 + 157601287591422x5 + 59099363823325x4 - 42232493776557x3 - 6358323449919x2 + 3052649440546x - 157964821171 \( 421^{34} \) $C_{35}$ (as 35T1) n/a
35.35.705...625.1 x35 - 175x33 - 70x32 + 13125x31 + 9702x30 - 556640x29 - 573225x28 + 14844900x27 + 19050185x26 - 261854635x25 - 394847250x24 + 3128435905x23 + 5347852195x22 - 25515383355x21 - 48297678121x20 + 141795944465x19 + 292585456625x18 - 533394487115x17 - 1187150912745x16 + 1349113537702x15 + 3207931617015x14 - 2286376450785x13 - 5710072444965x12 + 2606036871270x11 + 6560227221870x10 - 2026242763720x9 - 4691478893710x8 + 1084067118185x7 + 1962115542205x6 - 373976828869x5 - 432767079290x4 + 65717425060x3 + 43746645075x2 - 3865111915x - 1645272349 \( 5^{56}\cdot 7^{60} \) $C_{35}$ (as 35T1) n/a
35.35.313...761.1 x35 - x34 - 238x33 + 173x32 + 24286x31 - 16434x30 - 1418466x29 + 1081623x28 + 53047154x27 - 49719432x26 - 1339060322x25 + 1572006663x24 + 23323700077x23 - 34062526929x22 - 280163543133x21 + 504952475173x20 + 2262920124956x19 - 5071803868827x18 - 11476437360382x17 + 33655878701114x16 + 29727135340615x15 - 140118838407360x14 + 3247425380495x13 + 329245748251530x12 - 225104736115922x11 - 332674574789057x10 + 467468058300787x9 - 15355505673450x8 - 263968105366926x7 + 131023125506686x6 + 23123425964865x5 - 32591926570801x4 + 5190946345187x3 + 1696655472839x2 - 515233369184x + 22178194211 \( 491^{34} \) $C_{35}$ (as 35T1) n/a
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