curve #2912

y² + xy = x³ − 597872211893293896943612690x + 6922653506619993467506840401756825604100

a-invariants: [1, 0, 0, -597872211893293896943612690, 6922653506619993467506840401756825604100]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/5ℤ
conductor (N): 142464282826190789129133930
discriminant (Δ): -7025344603942946062994327764270921215295942312854190594956277175699278322073600000
Faltings height: 14.4192
naive height: 196.9944
primes of bad reduction: 2, 3, 5, 7, 11, 17, 19, 37, 41, 353, 34231, 10416255431
regulator: 418862.2959604844069834516978853757170106745884804016
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:28:03 UTC
last updated: 2026-09-26 20:28:03 UTC

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

(136948832900, 82708996863243207710)
(12658290255380, 37187096661453156110)
(-8085873615820, -105963703424465145490)
(1502180413580, 77639752721509657910)
(12034546795460, 38347087967452878110)
(4298443999850, 66574422404286487460)
(13688354493380, 36104952169567028510)

Commentary

Dujella - Lecacheux (2009). Source: https://dujella.github.io/tors/z5old678.html (curve entry 21). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:28:03 UTC · history