curve #3567

y² + xy + y = x³ − x² − 343568235666827280869353722405435309509095033209343428455x + 1987445525047374614284573584340458518204677324891968209570467476601215224715943094047

a-invariants: [1, -1, 1, -343568235666827280869353722405435309509095033209343428455, 1987445525047374614284573584340458518204677324891968209570467476601215224715943094047]
rank (lower bound): ≥ 30
torsion subgroup: trivial
conductor (N): 6925840361736399640390909690259280934153755186270204488096430032854975348893829584638104741798404370964279297025057425063922738987863619286650
discriminant (Δ): 889113819939497616421139368963170574460374056360215393178228564515530566048595570185813858033455762227856512688952631268673116991018274339686839577461989494353346336000000
Faltings height: 31.5184
naive height: 402.1505
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 67, 79, 97, 173, 28927, 831230681, 50021742476161825199, 7574758253056708808657430225336006865208286834932053923838202640122823630091154264111936712487
regulator: 145659953433185644601163636272026648497646891.19325196202562116995583998559039553671592755561662570
submitted by: Matej Jurasić
submitted at: 2026-09-28 18:38:14 UTC
last updated: 2026-09-28 18:38:14 UTC

Witness: 30 independent points log in to add more points →

(6524038092701966124764938099, 153871303164539634424774830749649809981150)
(14521781866150393670096206765, -246185116377831858778537750451811498016552)
(136743998593553360277963124249, 50119575006297739068758854739764927148479100)
(157166428436196655637764082299, 61888633747565287482407539878209396743890350)
(15195843797246767288754239939, 524942208752402775858663650660805253538030)
(144180636724882955059045453547/4, -48289310134304708693520638620804174945110095/8)
(21608063022445295098841137819, -2156985697872786590648659122205860466209610)
(-10927131971840241174026611229/9, 41852532965980663952522526127153819759898330/27)
(19762111862699654288153763269, 1707550244721642454174658715980151139619840)
(59629646855971552162208447491/9, -1198980568639495927622319616902434392896550/27)
(6389804542728476962881945703, -230227776313067849199831631340912164690054)
(-6668292004786459246414592701, -1995481341220378323805569594792013703417650)
(14312390490525024181817212499, 44469746549772641741895749881229468882350)
(304067039095186081276244223109/16, -97518617357067821145925181626612819633671475/64)
(33145231786884792235613272139, 5197437846208491549095099948832887968374830)
(7658761643106631226227698654739/361, -14135900537940070595874442479343119345311791150/6859)
(144191911267485662992704512819, 54317455929940342962347825441849726386415390)
(4187640643169377241348567978143231997101939/288231092116900, 1224591249700942436048908768705515784680237332089392719536683473/4893405896372694553000)
(-1614630369321998077117784348707032985961540023331/81719338641564005776, 761420758341246481107140406439765426039211506858206165807031628423135735/738732600191738679955453561024)
(33347920859435709018453494963483338347708119209849/2289747748992123945001, 29581908240596522239577093089949910827505346140730951373493622274577036850/109567426494349876461518746113749)
(48776887006291260388138731937327568171742818922529991/2526739115604925875255625, -6412411322564214644666557949532050773187742509316874672894811664006931489755686/4016433727550891405509102374657453125)
(40999532916660895319462359217695271572583827580003460883/10225526855018576524078061641, -849128987113107625808989967649489648766742586734380331487823324884839398299131588890/1034019051180502277867446255682412438229189)
(8605297042400867684822256165304157400320071506476723459/280380977454887023377508561, 21180591261010636260257736974539391607521499660813650371664341890361956806990411890/4694861858829895594355679017253203993191)
(4687532941969895923792643708853842267003160556587287682043/1950902945922756433319331481, 320925042433536774849240332839477700266785093925512531448190127289198534839498409765466/86169484888337133915569607201704650610371)
(224131229775583171420368605379398913157489982404977289898659/2489395358856329427923419248361, 103983877125732883644883299011227077610962351553826569386025159591473943434004871715208610/3927722651114567969214003617983420298504574859)
(788191464069492654292214627465778188774565509117490807244411/11584532103798861206465286136849, 675580506307079572121420296847338450393898974486413535841099175146142432121539440076352810/39429180083575523886727752691053108221608912007)
(-155744461419093632112176023695755850745482025546732559999339/17198567872807394623094726852449, 148862752989395237623631745796928039922910524965256404658849495015415672220858174306701040/71324449274439390255432973147038529266265330543)
(58221056190861088393934212544712301592720419323971647982955131/3488662174575781200481445053041049, 195670850450679882228961773140820980093167831885286539907362334973746611422908908075510794970/206057475463087221964495044613955303483203700555843)
(181930465957913162003774712500276093600154757239480470176971931/6411654615410707212193340273226049, -1993978381038265228266116103835543395686386497566454540877268170786635253870319288620775991370/513399190359581644094042034876575894462367680626657)
(92376720947355029712784011114267954893877862598461864864880435531/3118597252600760852763210281488636369, 23235815234756142449491410425786862202199723850666732279301394674243500124458455714530155506197250/5507302579490693222466175408653028780608870406196636903)

Commentary

Specialization at T = 82431/14059 of a rank-17 fibration of X1008 (2-neighbour of the one in curve#751).

last edited by Matej Jurasić at 2026-09-28 18:38:14 UTC · history