curve #2931

y² + xy = x³ − 1017843352326919892221795x + 583997132716712282566571150568433025

a-invariants: [1, 0, 0, -1017843352326919892221795, 583997132716712282566571150568433025]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/5ℤ
conductor (N): 1856561926508441474869470
discriminant (Δ): -79847328043998607095435278135800408772374744064751415262723013005414400000
Faltings height: 12.8809
naive height: 178.2336
primes of bad reduction: 2, 3, 5, 7, 11, 17, 23, 37, 47, 73, 16481, 982459601
regulator: 115262.6674560557768376904929488470510685063604784333
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:28:54 UTC
last updated: 2026-09-26 20:28:54 UTC

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

(60009577390, 723279229166022505)
(509759245670, 444527923405600505)
(-121890379090, -840387639572936215)
(207429320080, 617892786310079905)
(320127896840, 539410987983979505)
(-384838786210, -958492251841957495)
(704156584190, 465212037243711305)

Commentary

Dujella - Lecacheux (2009). Source: https://dujella.github.io/tors/z5old678.html (curve entry 24). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:28:54 UTC · history