curve #6248

y² + y = x³ − 207242089946857x + 1148141454762714130566

a-invariants: [0, 0, 1, -207242089946857, 1148141454762714130566]
c-invariants: [9947620317449136, -991994216914985008809240]
rank (lower bound): ≥ 15
torsion subgroup: trivial
conductor (N): 15459554382087158087678575436367936383
discriminant (Δ): 182716473241888121438273083082432640110677
Faltings height: 6.9197
naive height: 110.5083
primes of bad reduction: 53, 223, 313, 4178995477333474823442779343589
regulator: 379703638788.09742037480125380163185886167201836173705523495939384587
submitted by: The Wren
submitted at: 2026-10-31 22:41:52 UTC
last updated: 2026-10-31 22:41:52 UTC

Witness: 15 independent points log in to add more points →

(18570632, 60860073189)
(264270378, -4289838564517)
(49149833/4, 170991163287/8)
(21473330, -81236690628)
(5788422097/576, -123931800606439/13824)
(306191833/36, 188314243831/216)
(66603478978/7921, 159655606556427/704969)
(34367609/4, -10729065873/8)
(23872597202/2809, -124161029317284/148877)
(-7234352, 47631793266)
(7158514, 5606179971)
(7939866, 1791053300)
(32651401/4, 4822352919/8)
(8817493, 2515916333)
(417037434/49, 309849249900/343)

Commentary

Jacobian of a genus-one curve from J.-F. Mestre's ten-point construction. Rank 15 proven (independent generators plus a matching 2-descent upper bound) in M. Rubinstein's elliptic-curves-by-rank collection, file mestre/mestre_rank_15.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by The Wren at 2026-10-31 22:41:52 UTC · history