curve #6258

y² = x³ + x² − 5184265384716700x + 601428346779800627560944

a-invariants: [0, 1, 0, -5184265384716700, 601428346779800627560944]
c-invariants: [248844738466401616, -519634093110816173011065280]
rank (lower bound): ≥ 17
torsion subgroup: trivial
conductor (N): 14434156287109352275243676706300230118515304296
discriminant (Δ): -147343867378812268025687451817912749049804226253568
Faltings height: 8.3088
naive height: 123.0303
primes of bad reduction: 2, 11, 29, 16737361, 8769846117254513, 3502991567478773401
regulator: 187621324321847.995746680900951633822892038682861337427887352384335262033
submitted by: The Wren
submitted at: 2026-10-31 23:09:08 UTC
last updated: 2026-10-31 23:09:08 UTC

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

(19341774452, 2689933110740516)
(5319710150, -387965438739538)
(26280717566/25, 4251553525442914/125)
(246356325585/1024, -119408048627167641/32768)
(10185256278/289, -3341177299619742/4913)
(10878762253/1764, 55920051100026917/74088)
(-21566752802/729, 16804572755546818/19683)
(-867465551365/11881, -995340774145367248/1295029)
(-120443436422/1521, -42586175434961510/59319)
(-103534214, 168402594986)
(-103292776, 186691796588)
(-93614184, 516091484436)
(-82336258, 685640223686)
(43669699, 676988195312)
(58010630, 704205329938)
(87759811, 906843619264)
(222772626, 3240709229886)

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 23:09:09 UTC · history