curve #2393

y² + xy + y = x³ − 276541071824x + 55968993868661966

a-invariants: [1, 0, 1, -276541071824, 55968993868661966]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 235922610
discriminant (Δ): 248662901647450179098424462416400
Faltings height: 5.2472
naive height: 90.6505
primes of bad reduction: 2, 3, 5, 7, 11, 41, 47, 53
regulator: 4.550288010296718012881941162302374653213
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:58:47 UTC
last updated: 2026-09-26 19:58:47 UTC

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

(-393615, 322432567)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-44, q=3; A=(3q-p)(p+q)^3=-3652813, B=-(p+3q)(p-q)^3=-3633805. 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 19:58:47 UTC · history