curve #6252

y² + xy = x³ − x² − 39777038566710x + 1905227365682112803216

a-invariants: [1, -1, 0, -39777038566710, 1905227365682112803216]
c-invariants: [1909297851202089, -1646116435357505131569237]
rank (lower bound): ≥ 16
torsion subgroup: trivial
conductor (N): 1930969314026470623366215581134549103384590
discriminant (Δ): -1564085144361441204926634620718984773741517900
Faltings height: 7.3512
naive height: 111.5209
primes of bad reduction: 2, 3, 5, 24821, 40127, 32469846454211, 663432375663989923
regulator: 97846278285603.90392612413783800877315912887905724522472778765913834335
submitted by: The Wren
submitted at: 2026-10-31 22:53:49 UTC
last updated: 2026-10-31 22:53:49 UTC

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

(-101160782/121, -58592146576924/1331)
(30270406318, -5266579137440264)
(2781828352/289, -241421834401132/4913)
(177563532943/11236, -86086622666668409/1191016)
(562843003/961, 1292430290237416/29791)
(-57695486018/4489, 5153121974622718/300763)
(-309224726/25, -2807902104028/125)
(28632999167977/153664, 153143808602141561273/60236288)
(216869570101/625, 100977455769423274/15625)
(-12417920, 22012418164)
(3321082, 42539551348)
(42274147/4, 412968835013/8)
(14997376, 68416949452)
(28477063, 154471268101)
(29629850, 163507398546)
(-118524266/25, 5572615256192/125)

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 22:53:49 UTC · history