curve #377

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y² = x³ + x² − 54582530786918941306870296700466269980x + 155508120487725564589054990982409349995405123741445623600

a-invariants: [0, 1, 0, -54582530786918941306870296700466269980, 155508120487725564589054990982409349995405123741445623600]
rank (lower bound): ≥ 23
torsion subgroup: trivial
conductor (N): 346478779930321939361076024467070189800020825860952785510903285808190241857604974280 ★ record for rank ≥ 23
naive height: 272.2957
Faltings height: 20.4886
discriminant (Δ): -39589405100930217882581751340531373446377486872969881088300999340216951933611094263781118969234778283266988000000
primes of bad reduction: 2, 3, 5, 11, 13, 19, 23, 29, 37, 103, 21929, 1014557, 152895091, 485771053464014284495634549332962917335104529369969
regulator: 68140435839291680613427.4854470460090733353824821318411267622123584898197160795977727
submitted by: wgxli
submitted at: 2026-08-26 13:43:23 UTC
last updated: 2026-08-26 13:43:23 UTC

Witness: 23 independent points

(1331362935142675766560347804054194766/379507705105229089, 627329493861011273563930548271709122717639531671762150/233792673144681269973178063)
(-6550187282696468910, 15231494973531264489589992750)
(83726629201675626726/25, -400616286414441940925502419274/125)
(43061163060553562230/9, 53205321196251431722863760490/27)
(22076453212338106477950/5041, 243397921018830132579266679040890/357911)
(17482746853679560211834467710/3947231929, 198708718532017835015846616049457954165550/247992740403283)
(8549257141455960054211361438600/22877462075521, -1272156597494476523631238186970870451178291088460/109423793328237888319)
(320029450619077868290/81, 901541650602997954552811272750/729)
(-227688564018655800976837773/191739409, -39259215141054244099586642696516898872328/2655015596423)
(2405012145488034667516595058/415711321, 48958177664487605225830643325866593359546/8475938123869)
(1299687062433009294, -9314683310641698731706071610)
(532032560036787417049451880/121638841, 896528924183668533640561611561987737940/1341554777389)
(1970475433619800023387270/461041, -170275667491947264428333492908712430/313046839)
(18549043192051818290879249594139/4013847964681, 11257939935951837887214092018340858883806416880/8041579829471831579)
(2517514804547029815, -5835366302392291982765707350)
(-42030129297963350190/49, -4871271641240845596771203269950/343)
(6741922041100975422570/1681, 72586041245788259839944738388230/68921)
(2109759221701578909352420001500269/442335517587076, 17834754294113790994772568966070941511601836672005/9303100638064407752824)
(5637404130239738311061326756627560/1241374647523609, 49661827079826957921468204828874767426019940644500/43737535438272501867523)
(1195963462511779916974433098212947454/272994210687733441, -97476687375572310064158380877040016995556869261296630/142636329918039389545526239)
(20064673234222247714889210/4355569, -12278154330365594255624143005327825750/9090072503)
(10465794159738429081621854119710/1650872928769, 17004310932660414359323587324882278463467841750/2121145543876923647)
(39459263347124427668596935/6599761, 111042135983851927744323131027325825570/16954786009)

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