curve #2425

y² + xy + y = x³ − 28156888453x + 1797570899957756

a-invariants: [1, 0, 1, -28156888453, 1797570899957756]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 25571910
discriminant (Δ): 32768220065691079549952753062500
Faltings height: 4.8545
naive height: 83.7968
primes of bad reduction: 2, 3, 5, 7, 13, 17, 19, 29
regulator: 3.211103674384260056688816905753639578029
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:00:48 UTC
last updated: 2026-09-26 20:00:48 UTC

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

(-189095, 19080122)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-34, q=5; A=(3q-p)(p+q)^3=-1195061, B=-(p+3q)(p-q)^3=-1127061. 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 20:00:48 UTC · history