curve #2632

y² + xy + y = x³ − 148751791843x + 15205615546331306

a-invariants: [1, 0, 1, -148751791843, 15205615546331306]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 863272410
discriminant (Δ): 110769283052405048651183136095062500
Faltings height: 5.4294
naive height: 88.7902
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 89
regulator: 8.00740071367575713015450380841763243201902
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:14:06 UTC
last updated: 2026-09-26 20:14:06 UTC

Witness: 2 independent points log in to add more points →

(-428120, 20721662)
(-413435, 77905052)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-38, q=17; A=(3q-p)(p+q)^3=-824229, B=-(p+3q)(p-q)^3=2162875. 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 20:14:06 UTC · history