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Label Polynomial Discriminant Galois group Class group Regulator
35.35.876...281.1 $x^{35} - x^{34} - 34 x^{33} + 33 x^{32} + 528 x^{31} - 496 x^{30} - 4960 x^{29} + 4495 x^{28} + 31465 x^{27} - 27405 x^{26} - 142506 x^{25} + 118755 x^{24} + 475020 x^{23} - 376740 x^{22} - 1184040 x^{21} + 888030 x^{20} + 2220075 x^{19} - 1562275 x^{18} - 3124550 x^{17} + 2042975 x^{16} + 3268760 x^{15} - 1961256 x^{14} - 2496144 x^{13} + 1352078 x^{12} + 1352078 x^{11} - 646646 x^{10} - 497420 x^{9} + 203490 x^{8} + 116280 x^{7} - 38760 x^{6} - 15504 x^{5} + 3876 x^{4} + 969 x^{3} - 153 x^{2} - 18 x + 1$ $71^{34}$ $C_{35}$ (as 35T1) trivial $190122458612916620000$
35.35.107...681.1 $x^{35} - 2 x^{34} - 91 x^{33} + 186 x^{32} + 3529 x^{31} - 7282 x^{30} - 77406 x^{29} + 160015 x^{28} + 1074054 x^{27} - 2215841 x^{26} - 9975621 x^{25} + 20528466 x^{24} + 63908089 x^{23} - 131541229 x^{22} - 286306729 x^{21} + 593348019 x^{20} + 897545333 x^{19} - 1896502635 x^{18} - 1942677455 x^{17} + 4283320775 x^{16} + 2804705170 x^{15} - 6752081061 x^{14} - 2493142459 x^{13} + 7254188151 x^{12} + 1058706744 x^{11} - 5105442290 x^{10} + 147588576 x^{9} + 2206890342 x^{8} - 365733379 x^{7} - 523140235 x^{6} + 145322301 x^{5} + 51716162 x^{4} - 20476030 x^{3} - 56585 x^{2} + 426253 x - 7523$ $11^{28}\cdot 29^{30}$ $C_{35}$ (as 35T1) trivial $21825601175888975000000000$
35.35.145...169.1 $x^{35} - 2 x^{34} - 121 x^{33} + 124 x^{32} + 6435 x^{31} - 1020 x^{30} - 195036 x^{29} - 112597 x^{28} + 3683986 x^{27} + 4452851 x^{26} - 44769607 x^{25} - 80359740 x^{24} + 347984933 x^{23} + 850835561 x^{22} - 1630509423 x^{21} - 5621246939 x^{20} + 3615565971 x^{19} + 23234081997 x^{18} + 3088781711 x^{17} - 57619940147 x^{16} - 39347873390 x^{15} + 76695393961 x^{14} + 92864249975 x^{13} - 38675667681 x^{12} - 94158719636 x^{11} - 10380297650 x^{10} + 42855721796 x^{9} + 16263455858 x^{8} - 7226936109 x^{7} - 4634581071 x^{6} - 47622511 x^{5} + 349101928 x^{4} + 70736582 x^{3} + 5060011 x^{2} + 136327 x + 859$ $11^{28}\cdot 43^{30}$ $C_{35}$ (as 35T1) trivial $8063096359873239000000000000$
35.35.106...241.1 $x^{35} - x^{34} - 102 x^{33} + 231 x^{32} + 4336 x^{31} - 15350 x^{30} - 93149 x^{29} + 492148 x^{28} + 885684 x^{27} - 8797227 x^{26} + 2494886 x^{25} + 89830596 x^{24} - 154446290 x^{23} - 471756827 x^{22} + 1664362308 x^{21} + 444168124 x^{20} - 8565464505 x^{19} + 8653560326 x^{18} + 19862461891 x^{17} - 47903559470 x^{16} + 736744022 x^{15} + 100720726682 x^{14} - 96083394992 x^{13} - 62920019542 x^{12} + 165504701751 x^{11} - 60624002242 x^{10} - 87564669300 x^{9} + 86642725878 x^{8} - 451900172 x^{7} - 32473918206 x^{6} + 11871839347 x^{5} + 3432884529 x^{4} - 2696920777 x^{3} + 146105313 x^{2} + 172726939 x - 27756643$ $211^{34}$ $C_{35}$ (as 35T1) trivial $24168639235544094000000000000$
35.35.732...081.1 $x^{35} - 7 x^{34} - 112 x^{33} + 742 x^{32} + 5845 x^{31} - 34447 x^{30} - 188041 x^{29} + 918544 x^{28} + 4120599 x^{27} - 15488536 x^{26} - 63930916 x^{25} + 170889838 x^{24} + 709660070 x^{23} - 1224719069 x^{22} - 5607885533 x^{21} + 5331715046 x^{20} + 31035849173 x^{19} - 10542390278 x^{18} - 116936498434 x^{17} - 15812866636 x^{16} + 286852619543 x^{15} + 146466192098 x^{14} - 426702558436 x^{13} - 357822103121 x^{12} + 338413935629 x^{11} + 421000631443 x^{10} - 94811511375 x^{9} - 240823440823 x^{8} - 25297046987 x^{7} + 58988457696 x^{6} + 13678049308 x^{5} - 6371815744 x^{4} - 1687698845 x^{3} + 280068103 x^{2} + 55092156 x - 2660503$ $7^{60}\cdot 11^{28}$ $C_{35}$ (as 35T1) trivial $103376387230934820000000000000$
35.35.103...625.1 $x^{35} - 5 x^{34} - 120 x^{33} + 560 x^{32} + 6265 x^{31} - 27063 x^{30} - 188895 x^{29} + 746800 x^{28} + 3677845 x^{27} - 13130310 x^{26} - 48923530 x^{25} + 155517810 x^{24} + 458129250 x^{23} - 1279983515 x^{22} - 3063191465 x^{21} + 7446901792 x^{20} + 14674072475 x^{19} - 30859715040 x^{18} - 50096318770 x^{17} + 91037787910 x^{16} + 120155286235 x^{15} - 189447334860 x^{14} - 197298653000 x^{13} + 272612081065 x^{12} + 212356717105 x^{11} - 261877354307 x^{10} - 139209319745 x^{9} + 158110983885 x^{8} + 48766657725 x^{7} - 53789658890 x^{6} - 7150843552 x^{5} + 8233276160 x^{4} + 456884545 x^{3} - 363355535 x^{2} - 50594420 x - 1782107$ $5^{56}\cdot 29^{30}$ $C_{35}$ (as 35T1) trivial $2479808589614732200000000000000$
35.35.180...921.1 $x^{35} - x^{34} - 136 x^{33} + 115 x^{32} + 7922 x^{31} - 5864 x^{30} - 262379 x^{29} + 176786 x^{28} + 5536174 x^{27} - 3463751 x^{26} - 78912031 x^{25} + 45605901 x^{24} + 785104244 x^{23} - 406720184 x^{22} - 5548252572 x^{21} + 2436396552 x^{20} + 28031325744 x^{19} - 9529852980 x^{18} - 100888672963 x^{17} + 22693210859 x^{16} + 254967397769 x^{15} - 26498170926 x^{14} - 440501997963 x^{13} - 3333796454 x^{12} + 500538383949 x^{11} + 44640325883 x^{10} - 358942724140 x^{9} - 43476115800 x^{8} + 159203701176 x^{7} + 16418359222 x^{6} - 42718375268 x^{5} - 1999390430 x^{4} + 6413147106 x^{3} - 204719982 x^{2} - 415325205 x + 48529823$ $281^{34}$ $C_{35}$ (as 35T1) trivial $6612930761186456000000000000000$
35.35.497...681.1 $x^{35} - 2 x^{34} - 181 x^{33} + 470 x^{32} + 14259 x^{31} - 45478 x^{30} - 638530 x^{29} + 2447153 x^{28} + 17767052 x^{27} - 82345759 x^{26} - 312539633 x^{25} + 1833247298 x^{24} + 3264215879 x^{23} - 27715265019 x^{22} - 13487454777 x^{21} + 286033632049 x^{20} - 123264134993 x^{19} - 1983204888009 x^{18} + 2337315606897 x^{17} + 8777927035267 x^{16} - 17238219604018 x^{15} - 21289728738165 x^{14} + 71563023595709 x^{13} + 8692436762607 x^{12} - 169783075654432 x^{11} + 94786315419610 x^{10} + 202072200901306 x^{9} - 240242794434974 x^{8} - 58566297948415 x^{7} + 212040077699383 x^{6} - 73316281317651 x^{5} - 51014137537536 x^{4} + 37974482870362 x^{3} - 1868368126575 x^{2} - 3872034006535 x + 804494744591$ $11^{28}\cdot 71^{30}$ $C_{35}$ (as 35T1) trivial $14144996650663707000000000000000$
35.35.426...641.1 $x^{35} - 2 x^{34} - 147 x^{33} + 384 x^{32} + 8999 x^{31} - 28384 x^{30} - 300934 x^{29} + 1116603 x^{28} + 6027458 x^{27} - 26518095 x^{26} - 73782007 x^{25} + 404019590 x^{24} + 521840181 x^{23} - 4069268247 x^{22} - 1503940067 x^{21} + 27441438677 x^{20} - 6471979421 x^{19} - 124171354119 x^{18} + 81524582969 x^{17} + 375114725905 x^{16} - 364687984188 x^{15} - 747339096335 x^{14} + 926308497451 x^{13} + 961292881275 x^{12} - 1451786049968 x^{11} - 771321612374 x^{10} + 1427632011474 x^{9} + 365928432486 x^{8} - 868346663001 x^{7} - 97103750919 x^{6} + 312022190475 x^{5} + 17703737306 x^{4} - 59996070990 x^{3} - 4579250401 x^{2} + 4824514261 x + 750695467$ $29^{30}\cdot 31^{28}$ $C_{35}$ (as 35T1) trivial $51550321315774970000000000000000$
35.35.168...681.1 $x^{35} - x^{34} - 204 x^{33} + 437 x^{32} + 17534 x^{31} - 54290 x^{30} - 824862 x^{29} + 3275941 x^{28} + 23317913 x^{27} - 115242097 x^{26} - 407103864 x^{25} + 2577740505 x^{24} + 4218284220 x^{23} - 38412158946 x^{22} - 19912715245 x^{21} + 391393011501 x^{20} - 73963916883 x^{19} - 2766871309456 x^{18} + 1816877075105 x^{17} + 13678303310453 x^{16} - 13286645514747 x^{15} - 47446655533795 x^{14} + 55834172665771 x^{13} + 115251505419203 x^{12} - 148585020568878 x^{11} - 193921735357495 x^{10} + 253198008831294 x^{9} + 219700193289987 x^{8} - 266521489745621 x^{7} - 156623228737724 x^{6} + 157601287591422 x^{5} + 59099363823325 x^{4} - 42232493776557 x^{3} - 6358323449919 x^{2} + 3052649440546 x - 157964821171$ $421^{34}$ $C_{35}$ (as 35T1) not computed
35.35.705...625.1 $x^{35} - 175 x^{33} - 70 x^{32} + 13125 x^{31} + 9702 x^{30} - 556640 x^{29} - 573225 x^{28} + 14844900 x^{27} + 19050185 x^{26} - 261854635 x^{25} - 394847250 x^{24} + 3128435905 x^{23} + 5347852195 x^{22} - 25515383355 x^{21} - 48297678121 x^{20} + 141795944465 x^{19} + 292585456625 x^{18} - 533394487115 x^{17} - 1187150912745 x^{16} + 1349113537702 x^{15} + 3207931617015 x^{14} - 2286376450785 x^{13} - 5710072444965 x^{12} + 2606036871270 x^{11} + 6560227221870 x^{10} - 2026242763720 x^{9} - 4691478893710 x^{8} + 1084067118185 x^{7} + 1962115542205 x^{6} - 373976828869 x^{5} - 432767079290 x^{4} + 65717425060 x^{3} + 43746645075 x^{2} - 3865111915 x - 1645272349$ $5^{56}\cdot 7^{60}$ $C_{35}$ (as 35T1) not computed
35.35.313...761.1 $x^{35} - x^{34} - 238 x^{33} + 173 x^{32} + 24286 x^{31} - 16434 x^{30} - 1418466 x^{29} + 1081623 x^{28} + 53047154 x^{27} - 49719432 x^{26} - 1339060322 x^{25} + 1572006663 x^{24} + 23323700077 x^{23} - 34062526929 x^{22} - 280163543133 x^{21} + 504952475173 x^{20} + 2262920124956 x^{19} - 5071803868827 x^{18} - 11476437360382 x^{17} + 33655878701114 x^{16} + 29727135340615 x^{15} - 140118838407360 x^{14} + 3247425380495 x^{13} + 329245748251530 x^{12} - 225104736115922 x^{11} - 332674574789057 x^{10} + 467468058300787 x^{9} - 15355505673450 x^{8} - 263968105366926 x^{7} + 131023125506686 x^{6} + 23123425964865 x^{5} - 32591926570801 x^{4} + 5190946345187 x^{3} + 1696655472839 x^{2} - 515233369184 x + 22178194211$ $491^{34}$ $C_{35}$ (as 35T1) not computed
35.35.126...761.1 $x^{35} - x^{34} - 318 x^{33} + 317 x^{32} + 43270 x^{31} - 44942 x^{30} - 3310862 x^{29} + 3668450 x^{28} + 157558384 x^{27} - 185600815 x^{26} - 4874575299 x^{25} + 5926292085 x^{24} + 99830505974 x^{23} - 118520702371 x^{22} - 1360601812909 x^{21} + 1450494933204 x^{20} + 12343981755562 x^{19} - 10508898867517 x^{18} - 74032961784647 x^{17} + 42704647887631 x^{16} + 287498465575547 x^{15} - 88218677962585 x^{14} - 700005264128682 x^{13} + 73955415615078 x^{12} + 1050451088258971 x^{11} + 22743315993476 x^{10} - 954692059092009 x^{9} - 86158127076259 x^{8} + 507760932924813 x^{7} + 58457767140166 x^{6} - 148182973420093 x^{5} - 15997207615891 x^{4} + 21209750016487 x^{3} + 1792377500264 x^{2} - 1107362185802 x - 70566500269$ $11^{28}\cdot 71^{34}$ $C_{35}$ (as 35T1) not computed
35.35.126...761.2 $x^{35} - x^{34} - 318 x^{33} + 317 x^{32} + 43270 x^{31} - 41818 x^{30} - 3317891 x^{29} + 3042088 x^{28} + 159164901 x^{27} - 136621962 x^{26} - 5023426089 x^{25} + 4032403792 x^{24} + 106965005797 x^{23} - 81468720613 x^{22} - 1551807041244 x^{21} + 1156997268458 x^{20} + 15303293963931 x^{19} - 11690419597357 x^{18} - 101072209771211 x^{17} + 83452569029724 x^{16} + 433154733639634 x^{15} - 407573882251178 x^{14} - 1135196506881278 x^{13} + 1277269182336892 x^{12} + 1617541808283635 x^{11} - 2309930700089253 x^{10} - 924309789556182 x^{9} + 2069849763180324 x^{8} - 31527404480477 x^{7} - 820763459240694 x^{6} + 127806137756499 x^{5} + 158731707572343 x^{4} - 27752306968552 x^{3} - 15190639870341 x^{2} + 1694951868683 x + 570788981531$ $11^{28}\cdot 71^{34}$ $C_{35}$ (as 35T1) $[5]$ $157977180088699470000000000000000000$
35.35.126...761.3 $x^{35} - x^{34} - 318 x^{33} + 317 x^{32} + 43270 x^{31} - 41818 x^{30} - 3353817 x^{29} + 3156114 x^{28} + 166192339 x^{27} - 157145080 x^{26} - 5594925182 x^{25} + 5553139657 x^{24} + 132537042001 x^{23} - 143747356164 x^{22} - 2252399370560 x^{21} + 2747314382206 x^{20} + 27657159444349 x^{19} - 38620988612168 x^{18} - 244180261677833 x^{17} + 395369814537955 x^{16} + 1519547919984606 x^{15} - 2901002331604206 x^{14} - 6371608271240383 x^{13} + 14883656073565122 x^{12} + 16180433463310790 x^{11} - 51293588370254988 x^{10} - 16526681995068582 x^{9} + 110658425051062629 x^{8} - 25418996200662981 x^{7} - 128875911473035575 x^{6} + 88155825611539800 x^{5} + 48451033704977875 x^{4} - 69199250340085625 x^{3} + 22106764555181250 x^{2} - 1526617836093750 x + 26825251953125$ $11^{28}\cdot 71^{34}$ $C_{35}$ (as 35T1) $[5]$ $36127925528854230000000000000000000000$
35.35.126...761.4 $x^{35} - x^{34} - 318 x^{33} + 317 x^{32} + 43270 x^{31} - 41818 x^{30} - 3353036 x^{29} + 3096758 x^{28} + 166166566 x^{27} - 145170007 x^{26} - 5600988866 x^{25} + 4593389844 x^{24} + 133171453768 x^{23} - 102102398535 x^{22} - 2282944257911 x^{21} + 1638124605302 x^{20} + 28560705702931 x^{19} - 19324319690803 x^{18} - 261900749526875 x^{17} + 169477060925121 x^{16} + 1755651678876684 x^{15} - 1108105620618738 x^{14} - 8516264883934154 x^{13} + 5359995142956561 x^{12} + 29320125282559895 x^{11} - 18773007445519678 x^{10} - 69400335603008637 x^{9} + 45772424175347775 x^{8} + 107388225946229433 x^{7} - 72951536197993983 x^{6} - 100320065201875889 x^{5} + 69063464529667601 x^{4} + 49691531632300546 x^{3} - 33657568555946358 x^{2} - 9859582545986606 x + 6356574139799311$ $11^{28}\cdot 71^{34}$ $C_{35}$ (as 35T1) not computed
35.35.158...321.1 $x^{35} - x^{34} - 306 x^{33} + 619 x^{32} + 39918 x^{31} - 119144 x^{30} - 2870165 x^{29} + 11295452 x^{28} + 122756704 x^{27} - 613544599 x^{26} - 3125202817 x^{25} + 20310067731 x^{24} + 43327481459 x^{23} - 419360814437 x^{22} - 191553090102 x^{21} + 5427052738052 x^{20} - 3059836998013 x^{19} - 43960753448720 x^{18} + 54505011780373 x^{17} + 222701516749019 x^{16} - 391917990416865 x^{15} - 698605421390367 x^{14} + 1577201532402182 x^{13} + 1315814631610304 x^{12} - 3783939420646960 x^{11} - 1378428158842980 x^{10} + 5373712881752846 x^{9} + 635624897449864 x^{8} - 4223346678884758 x^{7} + 43477310737712 x^{6} + 1553138017862548 x^{5} - 130695356406557 x^{4} - 188318564137938 x^{3} + 16596019359307 x^{2} + 7161902265758 x - 508905734879$ $631^{34}$ $C_{35}$ (as 35T1) not computed
35.35.568...801.1 $x^{35} - x^{34} - 340 x^{33} + 207 x^{32} + 49944 x^{31} - 7990 x^{30} - 4183428 x^{29} - 1339227 x^{28} + 221817672 x^{27} + 178815786 x^{26} - 7804094139 x^{25} - 9996231518 x^{24} + 185580726182 x^{23} + 322903995482 x^{22} - 2981584862193 x^{21} - 6551278786057 x^{20} + 31810889107359 x^{19} + 85878214206021 x^{18} - 216446344956036 x^{17} - 730867798256917 x^{16} + 852222286700216 x^{15} + 3989130935173737 x^{14} - 1327554661734521 x^{13} - 13529921808469511 x^{12} - 2729204989489053 x^{11} + 26934334580298285 x^{10} + 15036045834469876 x^{9} - 28728875944213888 x^{8} - 23793327645401459 x^{7} + 14049593564031596 x^{6} + 16328881779981425 x^{5} - 1803371342400548 x^{4} - 4724492426296478 x^{3} - 461680786104416 x^{2} + 415380586464395 x + 62827062941873$ $701^{34}$ $C_{35}$ (as 35T1) not computed
35.35.420...041.1 $x^{35} - x^{34} - 442 x^{33} + 217 x^{32} + 85220 x^{31} - 2238 x^{30} - 9436469 x^{29} - 3733012 x^{28} + 665405852 x^{27} + 518480639 x^{26} - 31337617705 x^{25} - 35516568513 x^{24} + 1006061093515 x^{23} + 1481171485580 x^{22} - 22064557661077 x^{21} - 40105273516115 x^{20} + 325564905075174 x^{19} + 718606613070565 x^{18} - 3104378497697910 x^{17} - 8465726517162874 x^{16} + 17359496453493293 x^{15} + 63647428757599053 x^{14} - 39918422702860182 x^{13} - 286218584896036781 x^{12} - 91666282635987596 x^{11} + 665845380121245570 x^{10} + 709902006827264737 x^{9} - 485410723276588718 x^{8} - 1192541413062255796 x^{7} - 419664407183170897 x^{6} + 445121936202637191 x^{5} + 400491751414674915 x^{4} + 50965550537459510 x^{3} - 54268060119801121 x^{2} - 22150406599986335 x - 2362460740247707$ $911^{34}$ $C_{35}$ (as 35T1) not computed
  displayed columns for results