curve #2512

y² + xy = x³ − 67776436x + 149241506960

a-invariants: [1, 0, 0, -67776436, 149241506960]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 1345890
discriminant (Δ): 10303141811083180396646400
Faltings height: 3.5049
naive height: 65.7088
primes of bad reduction: 2, 3, 5, 7, 13, 17, 29
regulator: 1.851685272821862139489803122057492839938
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:06:12 UTC
last updated: 2026-09-26 20:06:12 UTC

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

(-9016, 170156)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-17, q=4; A=(3q-p)(p+q)^3=-63713, B=-(p+3q)(p-q)^3=-46305. 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 20:06:12 UTC · history