curve #3055

y² + xy = x³ + 12370764835409459885826379544x + 1795055346226263534415826963120427011109440

a-invariants: [1, 0, 0, 12370764835409459885826379544, 1795055346226263534415826963120427011109440]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/6ℤ
conductor (N): 29700487374913942444634217870
discriminant (Δ): -1513163527746780070164665422564022377930991838214347310087572831655175842583509183426560
Faltings height: 15.4099
naive height: 208.1104
primes of bad reduction: 2, 3, 5, 11, 13, 17, 19, 23, 53, 83, 139, 163, 283, 401, 859, 95917
regulator: 41445186.6844584197950465450100264613192219531398431283
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:35:10 UTC
last updated: 2026-09-26 20:35:10 UTC

Witness: 8 independent points log in to add more points →

(-56977005345494, -951439538990147868830)
(-88177687531336, -136460691923638786600)
(61269766750790, 1668237052561641052790)
(57375133290296, 1641250460574949681904)
(3414484775543894, 199630932637620976515140)
(-47496752261296, -1048968183674705543080)
(279283600210559/4, 13854482876787646623025/8)
(-3211280688799924/49, -287556207376563099439660/343)

Commentary

Dujella - Peral (2020). Source: https://dujella.github.io/tors/z6old678.html (curve entry 50). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:35:10 UTC · history