curve #6257

y² = x³ − x² − 2210882042810510x + 40020845245008628896561

a-invariants: [0, -1, 0, -2210882042810510, 40020845245008628896561]
c-invariants: [106122338054904496, -34578009654953427037201760]
rank (lower bound): ≥ 16
torsion subgroup: trivial
conductor (N): 326491505507877704753301865214116989688788
discriminant (Δ): -286006558824900869363892433927566482967378288
Faltings height: 7.5198
naive height: 117.6105
primes of bad reduction: 2, 3, 73, 372707198068353544238929069879128983663
regulator: 6960818758360.330257427841600636257534331898247935265720605420026347990
submitted by: The Wren
submitted at: 2026-10-31 23:06:16 UTC
last updated: 2026-10-31 23:06:16 UTC

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

(286183978, -4779762837907)
(124632690, -1304005575669)
(689155949/100, 158466794598057/1000)
(1342811702/121, 172784474661195/1331)
(85175197/4, 407758847039/8)
(2752719792/169, -200527103467101/2197)
(38296873382/1849, -4436776247332869/79507)
(59863620140/2209, 301857604673637/103823)
(157225987025/3136, 41259659907732729/175616)
(-29320954, 282202503639)
(13008912, 116022397065)
(19963914, 61965803187)
(25827128, 12159461007)
(28730411, 14711390919)
(108472021/4, 23104264429/8)
(435567449/16, 189231932907/64)

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 23:06:16 UTC · history