curve #1864

y² + xy = x³ − 20479875863023306350365471832619956549325x + 993933033268419130390510321136309839840432436349373683027857

a-invariants: [1, 0, 0, -20479875863023306350365471832619956549325, 993933033268419130390510321136309839840432436349373683027857]
rank (lower bound): ≥ 23
torsion subgroup: trivial
conductor (N): 46632308659789023761800491518113829921375389884997240603399830478705777777014751263390
discriminant (Δ): 122971775282037573713034156349890713068733807351191240336313354484944384544581706830747929759355806788900369847235563200000
Faltings height: 22.1554
naive height: 290.0744
primes of bad reduction: 2, 3, 5, 11, 17, 23, 29, 31, 37, 41, 43, 67, 107, 109, 342901651825974771223139542799809602485180165120443571159354951819
regulator: 50666021698425798777684.7547881373031546996384224225355882227464416794983533439077423
submitted by: Ritik Jain
submitted at: 2026-09-25 17:16:32 UTC
last updated: 2026-09-25 17:16:32 UTC

Witness: 23 independent points log in to add more points →

(17909582657477446581430055934734343280818603389978/168945818672808172834722421561, -8270876430691533554867418385839261129034747212770136226083839600952565381/69441832273785725174311020560275572551827309)
(-154149030224734494436, 698576101810732695767110386533)
(-724936607970511328922544/4489, 90040387345048122473818251673116749/300763)
(54857330773524480242, -188534721523105475936741689777)
(-13139829895597338135361/196, -3943731890263345401289749483731993/2744)
(-109986536282361555028, -1384172068752982010099885522635)
(-46211595482389017269194/289, -2085821591255634112257302442598301/4913)
(-1028506445884598574694/25, 166153621690397257017045953460139/125)
(-88634836580143240133461324/2640625, 5501108897145808492369279740079070590951/4291015625)
(-22623263711459724521745956/2134521, 3430110302253275375400470497199063449793/3118535181)
(42642310896409163055269/400, 1192306157307276437444654479110013/8000)
(24328980653659245291056/169, 2228718160876404044128754083826051/2197)
(-31278686860170990129908011/250000, 158003105400488863033023571883817722263/125000000)
(-1640020383135400758882061/16900, -3159005810791057544821230017238539197/2197000)
(-2830761430426862590226/25, -170529304643912674812941168673553/125)
(-11737368080297073509142673553458/440021282281, -360006262646402150049540621378202943150143736297/291884157409560821)
(10543669681903211659803029834/12327121, -1068259334825548393332655167705164353693687/43280521831)
(-2022387557418307607525479391134/20372709289, 4162114727908278373619363668882956536567115691/2907857914946837)
(882843239394263997591623718949818675394/46262108340386925561, 245766473105990700558858603265160553609099535222258093345757/314657532024507617190958435059)
(-1816701127397241344997639317695798864/59718088350885409, 18394753249104027135727304566918064962985464282355639929/14593479267703402368089423)
(4308980407754200907867072055274/78876160801, 4327400411922227614652261181371606755505446807/22152290884800049)
(920473371258606045380067178015812614/15978489223790401, 147334780896884853815775110732774502344290089692718967/2019777691768421394535649)
(19670823136231651590297926/499849, 176316113428005320561317686404186958049/353393243)

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