curve #2916

y² + xy = x³ − 533024166437861795831860x + 150145561559705338985839395548651600

a-invariants: [1, 0, 0, -533024166437861795831860, 150145561559705338985839395548651600]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/6ℤ
conductor (N): 4290426777866593139490
discriminant (Δ): -46711743185348559156914365269279728565638561159211350855833734375000000
Faltings height: 12.4328
naive height: 175.5170
primes of bad reduction: 2, 3, 5, 11, 13, 17, 23, 29, 31, 41, 101, 113, 373, 16301
regulator: 25290.20144692118189331265185275928133539878192244612
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:28:14 UTC
last updated: 2026-09-26 20:28:14 UTC

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

(225881035820, 203151228866431340)
(-199633635190, -498596928696485410)
(379553028866, 50131880774897702)
(268669162916, 162270575082307472)
(329053583870, 101885757234320840)
(316093339430, 115076505790470290)
(390843022490, 39003503812839320)

Commentary

Eroshkin (2007). Source: https://dujella.github.io/tors/z6old678.html (curve entry 129). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:28:14 UTC · history