curve #6253

y² + xy = x³ + x² − 465941069887437x + 3968942817587930552745

a-invariants: [1, 1, 0, -465941069887437, 3968942817587930552745]
c-invariants: [22365171354597001, -3429166762134757157049125]
rank (lower bound): ≥ 16
torsion subgroup: trivial
conductor (N): 1491350913958806556224626733815272488356514
discriminant (Δ): -331079902898855055481867134906990492415146108
Faltings height: 7.3211
naive height: 112.9887
primes of bad reduction: 2, 3, 37, 9181, 526528998929, 1389679297145768871252763
regulator: 81140308898217.35721291961130848947083285589720387996619647341181935168
submitted by: The Wren
submitted at: 2026-10-31 22:55:50 UTC
last updated: 2026-10-31 22:55:50 UTC

Witness: 16 independent points log in to add more points →

(464752260, 10008335448795)
(1276281816, -45589438487595)
(340556111/4, 6099849815687/8)
(16838090704/289, -2053065242516563/4913)
(74474310510/3721, -11710726782116835/226981)
(98741282313/6241, 11637044569297155/493039)
(13950167414/961, 483941192427699/29791)
(162497073901/11664, -16984737863493857/1259712)
(206806874379/16129, -20764786280478438/2048383)
(-24624276, 22625427387)
(-588928, 65139716467)
(8696296, 23967379795)
(10285941, 16260131154)
(14027301, 13890170985)
(19007604, 44484971739)
(185786732, 2515886046937)

Commentary

Jacobian of a genus-one curve from J.-F. Mestre's ten-point construction. Rank 16 proven (independent generators plus a matching 2-descent upper bound) in M. Rubinstein's elliptic-curves-by-rank collection, file mestre/mestre_rank_16.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by The Wren at 2026-10-31 22:55:50 UTC · history