curve #2395

y² + xy + y = x³ − 96335989338x + 11416013505220156

a-invariants: [1, 0, 1, -96335989338, 11416013505220156]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 71353590
discriminant (Δ): 919074336059490302254184102250000
Faltings height: 5.1465
naive height: 87.4869
primes of bad reduction: 2, 3, 5, 7, 11, 17, 23, 79
regulator: 4.584203522559305931238504736472638155104
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:58:56 UTC
last updated: 2026-09-26 19:58:56 UTC

Witness: 1 independent point log in to add more points →

(31130, 91893312)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-28, q=17; A=(3q-p)(p+q)^3=-105149, B=-(p+3q)(p-q)^3=2095875. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is claimed.

last edited by Natanael Wildner Fraga at 2026-09-26 19:58:56 UTC · history