curve #2280

y² + xy = x³ − 4239488003016x + 3355634702108404800

a-invariants: [1, 0, 0, -4239488003016, 3355634702108404800]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 110698770
discriminant (Δ): 12190667805087590255460370191936000000
Faltings height: 6.0183
naive height: 98.8400
primes of bad reduction: 2, 3, 5, 7, 13, 23, 41, 43
regulator: 4.387743993971722544617517290777089494464
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:51:42 UTC
last updated: 2026-09-26 19:51:42 UTC

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

(4927587/4, 396083163/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-41, q=28; A=(3q-p)(p+q)^3=-274625, B=-(p+3q)(p-q)^3=14125887. 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 19:51:43 UTC · history