curve #2917

y² + xy = x³ − 8534087264917869870206860x + 9595856169467846573498585790738776600

a-invariants: [1, 0, 0, -8534087264917869870206860, 9595856169467846573498585790738776600]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/6ℤ
conductor (N): 4290426777866593139490
discriminant (Δ): 532499342632862238402671218475882427778741806843164167261144894875000
Faltings height: 12.7794
naive height: 183.8319
primes of bad reduction: 2, 3, 5, 11, 13, 17, 23, 29, 31, 41, 101, 113, 373, 16301
regulator: 809286.4463014778205860048592882970027327610215182760
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:28:18 UTC
last updated: 2026-09-26 20:28:18 UTC

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

(1722615431570, -81250757342004910)
(2286630502310, 1427447255757189590)
(1688190716366, -3519647137227298)
(1641202994968526/961, -1422623481048758664148/29791)
(1694063356370, -16748607103426660)
(83121758894570/49, -7521783564329465530/343)
(26982105516245/16, 30614295287207885/64)

Commentary

2-isogenous image of D-z6old678-129, rational kernel x=-843254960680. 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 20:28:18 UTC · history