curve #2924

y² + xy = x³ − 279021136261247540446385495x + 1793387038596711777513523387558820786025

a-invariants: [1, 0, 0, -279021136261247540446385495, 1793387038596711777513523387558820786025]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/5ℤ
conductor (N): 68510733689193262725648390
discriminant (Δ): 830397002991485860541600591071614243527727105302650873541190745681163059200000
Faltings height: 13.9222
naive height: 194.2936
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 37, 41, 53, 79, 1229, 904816141
regulator: 159006.2506431748505432562568007566739562767276232925
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:28:36 UTC
last updated: 2026-09-26 20:28:36 UTC

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

(-5948999789450, -56945102666568630155)
(4319183174680, 25861542387494115115)
(-7446369281978, -58806391157676338363)
(9786751791190, 237729005307986005)
(-251236942310, -43167946288761192995)
(9892302676630, 1123837020359445205)
(5263206579862, 21694214378887910101)

Commentary

Dujella - Lecacheux (2009). Source: https://dujella.github.io/tors/z5old678.html (curve entry 18). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:28:36 UTC · history