curve #6251

y² = x³ − 282795214480012x + 1874931627060924262900

a-invariants: [0, 0, 0, -282795214480012, 1874931627060924262900]
c-invariants: [13574170295040576, -1619940925780638563145600]
rank (lower bound): ≥ 16
torsion subgroup: trivial
conductor (N): 130908082123329853454719245346731068283032
discriminant (Δ): -71213996675091440279367269468621701145969408
Faltings height: 7.1944
naive height: 111.4889
primes of bad reduction: 2, 17, 1291, 6997, 11213, 14967607, 634914494977021178191
regulator: 55815958947143.54044064231078859335501205588946324460494263071271732079
submitted by: The Wren
submitted at: 2026-10-31 22:52:32 UTC
last updated: 2026-10-31 22:52:32 UTC

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

(-110496006/49, -17154024965734/343)
(8646560918, -804015252596254)
(92609913/49, -12589550534329/343)
(17715291458/2401, -1621908295043254/117649)
(2610080364/289, 37271191205446/4913)
(1358575401/25, 47924222794351/125)
(239153789186/3721, 113306978025505262/226981)
(645385341668/4489, 515081674945547786/300763)
(227642683449/676, 108479840721149581/17576)
(-18860743, 22346636153)
(-17884350, 34817112490)
(-6364774, 58455282442)
(8207014, 10334960926)
(9463466, 6799274998)
(9738334, 6671861186)
(12399172, 16575500222)

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 22:52:33 UTC · history