curve #6262

y² + xy = x³ − x² − 177361205377121419x + 27357990751064154774723433

a-invariants: [1, -1, 0, -177361205377121419, 27357990751064154774723433]
c-invariants: [8513337858101828121, -23637303970609409363902819581]
rank (lower bound): ≥ 17
torsion subgroup: trivial
conductor (N): 60651665135316562258841403131729616719909227790
discriminant (Δ): 33737488731519837756480530492024599300449507958187500
Faltings height: 8.8349
naive height: 130.7645
primes of bad reduction: 2, 5, 89, 6173, 935531, 11800441654783406243093684846659597
regulator: 1558751710517180.40318049631403579781891486827020275870571068260551892342
submitted by: The Wren
submitted at: 2026-10-31 23:19:58 UTC
last updated: 2026-10-31 23:19:58 UTC

Witness: 17 independent points log in to add more points →

(11147704872, -1176181679102611)
(-483352753, 400703830239)
(175530932278/49, -73053830198954023/343)
(11121476963/4, -1160086771500463/8)
(243968369127/841, -13783471550135654/24389)
(287791052, -388653320411)
(14108213638/49, 137286878079077/343)
(1866027961777/6241, 506927076297187046/493039)
(1519962123292/4761, 594350317580544401/328509)
(14878147, 4972162920114)
(300621547, 1098738384114)
(411370022, 4899908700739)
(458199963, 6502762128371)
(2368360772, 113540669893989)
(-10234791722/289, 28476308615332267/4913)
(-7653658297/49, 2455544442020977/343)
(3132337917/16, 23852755199611/64)

Commentary

Jacobian of a genus-one curve from J.-F. Mestre's ten-point construction. Rank 17 proven (independent generators plus a matching 2-descent upper bound) in M. Rubinstein's elliptic-curves-by-rank collection, file mestre/mestre_rank_17.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by The Wren at 2026-10-31 23:19:58 UTC · history