curve #2932

y² + xy + y = x³ − x² − 1160203178077817x + 14812203727081601453184

a-invariants: [1, -1, 1, -1160203178077817, 14812203727081601453184]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 305760573831635505
discriminant (Δ): 5168453182530359667259286979376250185297265625
Faltings height: 7.5483
naive height: 115.6757
primes of bad reduction: 3, 5, 11, 17, 19, 29, 41, 67, 97, 263, 941
regulator: 6260.222633290468396315079053958922736648817391534860
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:28:58 UTC
last updated: 2026-09-26 20:28:58 UTC

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

(11956373, 51468318693)
(24947072, -37355491584)
(1182846533/49, 10124940487563/343)
(743084597/16, -15821671232601/64)
(701309642, -18551089938909)
(34154757, -122609446999)
(2080866713/49, -70407885885147/343)

Commentary

2-isogenous to curve#2100 via the rational 2-torsion point x=19608095. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.

last edited by Natanael Wildner Fraga at 2026-09-26 20:28:58 UTC · history