curve #2596

y² + xy = x³ − 18280996718320x − 29173844657593081600

a-invariants: [1, 0, 0, -18280996718320, -29173844657593081600]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 95285190
discriminant (Δ): 23321677450265704633176233571815424000000
Faltings height: 6.5174
naive height: 103.2243
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 167
regulator: 5.94930849278321093669791170938653611503356
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:11:41 UTC
last updated: 2026-09-26 20:11:41 UTC

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

(-2809660, 99152480)
(-2763328, 493139216)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-1, q=56; A=(3q-p)(p+q)^3=28117375, B=-(p+3q)(p-q)^3=30927231. 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 20:11:42 UTC · history