curve #6254

y² + y = x³ − 493017395385697x + 3964507434242866168176

a-invariants: [0, 0, 1, -493017395385697, 3964507434242866168176]
c-invariants: [23664834978513456, -3425334423185836369304280]
rank (lower bound): ≥ 16
torsion subgroup: trivial
conductor (N): 879611946669933635328146333627700440787788197
discriminant (Δ): 879611946669933635328146333627700440787788197
Faltings height: 7.3733
naive height: 113.1083
primes of bad reduction: 1249, 704252959703709876163447825162290184778053
regulator: 60845206382941.65285658117551590571103540635718686125461315826356221891
submitted by: The Wren
submitted at: 2026-10-31 23:01:33 UTC
last updated: 2026-10-31 23:01:33 UTC

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

(2188072286/25, -99314997592091/125)
(6516212112, -526005519030816)
(53144292560/361, -12118920420390187/6859)
(109113026962/441, -35901807583596310/9261)
(26897630552/3721, 6332707068732515/226981)
(25434065/4, -263724433259/8)
(4438264447/289, -19067804234561/4913)
(278967101674/5625, 134401789880424782/421875)
(215486867776/2025, 97996527295159024/91125)
(-6611715, 83277657912)
(7864144, 23952113631)
(39304329/4, 66358923415/8)
(15286058, 99016821)
(15404602, 5030893434)
(26768229, 99738460023)
(205879941, 2937516391479)

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 23:01:33 UTC · history