curve #6259

y² + xy = x³ − x² − 64694218377440094x + 6244331224280652146766824

a-invariants: [1, -1, 0, -64694218377440094, 6244331224280652146766824]
c-invariants: [3105322482117124521, -5395102163804532285279475605]
rank (lower bound): ≥ 17
torsion subgroup: trivial
conductor (N): 21839804528723346103136677719886089956839385598
discriminant (Δ): 484712621710485943413015425315151880502093323962012
Faltings height: 8.5252
naive height: 127.7389
primes of bad reduction: 2, 3, 137, 43261087, 204719045132382640207417557922377169
regulator: 11775561594857074.0451397073963289376140394931292631251562018659993037209
submitted by: The Wren
submitted at: 2026-10-31 23:15:51 UTC
last updated: 2026-10-31 23:15:51 UTC

Witness: 17 independent points log in to add more points →

(-20504129, 2749957431820)
(43055498233, -8933803873288610)
(-5215276459/25, -408142202753926/125)
(183220625, -736091161607)
(8647017838/49, -195059549343980/343)
(17763741241/1681, -162540922048881250/68921)
(55463093566/529, -9534214253469244/12167)
(1752213424483/10609, 277836090006680080/1092727)
(13462694602/81, 210104724736000/729)
(-123585532, 3514607475480)
(-94398332, 3392711304280)
(-18888317, 2731228470877)
(132161860, 51529500292)
(172119652, 456268617928)
(211543750, 1423065626518)
(8410958713/64, 56016795542225/512)
(243019371265/1849, 8644106675786794/79507)

Commentary

Jacobian of a genus-one curve from J.-F. Mestre's ten-point construction. Rank 17 proven (independent generators plus a matching 2-descent upper bound) in M. Rubinstein's elliptic-curves-by-rank collection, file mestre/mestre_rank_17.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by The Wren at 2026-10-31 23:15:51 UTC · history