curve #1265

y² + xy + y = x³ − 2405554531940373439938x + 45411808336440388180601009865088

a-invariants: [1, 0, 1, -2405554531940373439938, 45411808336440388180601009865088]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/6ℤ
conductor (N): 4439405348342065911810
discriminant (Δ): 8726586722143009618394172786299931378105531514198340859766500
Faltings height: 10.8850
naive height: 159.3098
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 23, 29, 79, 257, 523, 631, 1741
regulator: 139136.5607701913337395669248448595588737567435945850
submitted by: hdeping
submitted at: 2026-09-24 16:48:28 UTC
last updated: 2026-09-24 16:48:28 UTC

(28256512094, -9395249967795)
(-7432769009599/1225, -331510664303146305279/42875)
(28440265664, 32705849387520)
(1398461091744377834/177241, -1653740217997171357554326955/74618461)
(7888259054887466/25, -700602614926448778581451/125)
(1818198802441/64, -11493096991679825/512)
(13089458099242, -47356491185615489140)

Found by a Mestre-Nagao sieve over the Tate normal form family y^2+txy+(t+2)y=x^3 with torsion Z/6Z, at t=589163/23621.

last edited by hdeping at 2026-09-27 08:24:09 UTC · history