curve #2897

y² + xy + y = x³ − 17365711898125979011358x + 6836139894688677403723829903428118

a-invariants: [1, 0, 1, -17365711898125979011358, 6836139894688677403723829903428118]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/6ℤ
conductor (N): 320501413516974788372430
discriminant (Δ): -19853409044529694970783772847942138446203746054697503257401212739790750
Faltings height: 12.1692
naive height: 169.3382
primes of bad reduction: 2, 3, 5, 13, 17, 19, 23, 29, 41, 101, 179, 359, 2129, 6733
regulator: 1222680.395753877724230612065044726678401279690837801
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:27:22 UTC
last updated: 2026-09-26 20:27:22 UTC

Witness: 7 independent points log in to add more points →

(149314110078, 87017784915503143)
(177326219294, 96605779556465370)
(-177099713942/9, -2286285771684195250/27)
(715564341702, 600667546117091770)
(37270185318222069/309136, 13851928092030198781478395/171879616)
(7425434711962369/46656, -907196052548889286945685/10077696)
(994242042249814051689/3001286656, -31813765713612864910681011186485/164422488162304)

Commentary

2-isogenous image of D-z6old678-136, rational kernel x=110033611989. Source: https://dujella.github.io/tors/z6old678.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.

last edited by Natanael Wildner Fraga at 2026-09-26 20:27:22 UTC · history