curve #2240

y² + xy + y = x³ − 18001886422098x + 29275371201369652756

a-invariants: [1, 0, 1, -18001886422098, 29275371201369652756]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 9834099990
discriminant (Δ): 3120865821406250109489855778281740250000
Faltings height: 6.4268
naive height: 103.1781
primes of bad reduction: 2, 3, 5, 11, 13, 17, 19, 47, 151
regulator: 5.389067853517745636418739778542079982483
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:49:09 UTC
last updated: 2026-09-26 19:49:09 UTC

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

(-4891510, 543980952)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-52, q=33; A=(3q-p)(p+q)^3=-1035709, B=-(p+3q)(p-q)^3=28863875. 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 19:49:09 UTC · history