curve #6265

← home · all curves · JSON ↓

y² + xy = x³ − x² − 294885328460068384x + 61361567889172926730902388

a-invariants

[1, -1, 0, -294885328460068384, 61361567889172926730902388]

c-invariants

[14154495766083282441, -53016394592550177748124892261]

rank (lower bound)

≥ 17

torsion subgroup

trivial

conductor (N)

465029593840878488544983778334871243962968049070

discriminant (Δ)

14532174807527452767030743072964726373842751533437500

Faltings height

8.8551

naive height

132.2897

primes of bad reduction

2, 5, 15428303996049423811, 3014132946563368903261954937

regulator

273543072116664.905988698567109313810305761883648159650806019976694812016

submitted by

The Wren

submitted at

2026-10-31 23:25:00 UTC

later contributions

primes of bad reduction recorded · Maksym Voznyy · 2026-10-31 23:28:56 UTC

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

(442265127, -4177593577126)
(3899573304502, -7700620812233970876)
(-1336978709873/2601, -1164906802482272651/132651)
(2639708458/9, 8651493873398/27)
(1175386269688/3969, -18285051003727922/250047)
(47501872323/169, -1815220298149597/2197)
(452916866238/1369, -5949529059420028/50653)
(890069132058/529, 800469374021862958/12167)
(28764913281512/11881, 150684290206568049346/1295029)
(-594851498, 5127416782374)
(-200424173, 10602586107174)
(-81050198, 9204911653124)
(270258702, 1185560481374)
(290130002, 477663579124)
(350061302, 1015284573124)
(4994095377, 350919648351124)
(3833139643/9, 97439006210098/27)

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 23:25:00 UTC · history