curve #2541

y² + xy + y = x³ − 28888163x + 59752688906

a-invariants: [1, 0, 1, -28888163, 59752688906]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 510510
discriminant (Δ): 376831286146377562500
Faltings height: 2.9645
naive height: 63.1504
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17
regulator: 2.145785960008473432263213415500360265322
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:08:02 UTC
last updated: 2026-09-26 20:08:02 UTC

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

(-3525, 344962)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-14, q=1; A=(3q-p)(p+q)^3=-37349, B=-(p+3q)(p-q)^3=-37125. 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 20:08:02 UTC · history