curve #6321

y² + xy = x³ + x² − 2729855054914502x + 54909284376421418795016

a-invariants: [1, 1, 0, -2729855054914502, 54909284376421418795016]
c-invariants: [131033042635896121, -47441622683975925608114669]
rank (lower bound): ≥ 16
torsion subgroup: trivial
conductor (N): 141203664385549654650538839647975847667590
discriminant (Δ): -529513741445811204939520648679909428753462500
Faltings height: 7.5719
naive height: 118.2431
primes of bad reduction: 2, 3, 5, 4706788812851655155017961321599194922253
regulator: 40999870532799.17497547635919190788848096872979887743106457747167883030
submitted by: The Wren
submitted at: 2026-11-01 00:11:30 UTC
last updated: 2026-11-01 00:11:30 UTC

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

(-72271363/16, 16584392286401/64)
(688217657, -18004399905316)
(-5981033401/100, 65028026850887/1000)
(16524268883/484, -413176289696653/10648)
(768041476/25, -785898657716/125)
(43676353443/1444, -189020301907197/54872)
(51698399662/1681, 449714946392584/68921)
(237414955097/4096, 79251351993506621/262144)
(355046345607/5476, 157178212188665991/405224)
(-238238497/4, 631157116147/8)
(18064567, 107185276139)
(24974132, 48050724884)
(117959903/4, 57648008947/8)
(30049057, 3504346059)
(30082007, 3418812734)
(32728442, 24933255044)

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 2026-11-01 00:11:30 UTC · history