curve #2935

y² + xy = x³ − 104247069206207225692790x + 13077998295796069821444447267212100

a-invariants: [1, 0, 0, -104247069206207225692790, 13077998295796069821444447267212100]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/5ℤ
conductor (N): 80529780156718252850490
discriminant (Δ): -1381107453326274305673116527361670366762486464846925051472469936100000
Faltings height: 12.0819
naive height: 170.6356
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 23, 29, 61, 1090099, 3182189
regulator: 68260.87170051390637158383520048999615737394153661001
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:29:05 UTC
last updated: 2026-09-26 20:29:05 UTC

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

(116272397230, 50287710041280910)
(135871495882, 37711009485178696)
(-209059328720, -160420326788933090)
(111490681480, 53303507561825110)
(179713181770, 12148632954661870)
(174119066110, 14333157496354510)
(130979046880, 40875709416792910)

Commentary

Dujella - Lecacheux (2009). Source: https://dujella.github.io/tors/z5old678.html (curve entry 27). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:29:05 UTC · history