curve #2602

y² + xy + y = x³ − x² − 11446149312113x + 14896396946060354081

a-invariants: [1, -1, 1, -11446149312113, 14896396946060354081]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 71981910
discriminant (Δ): 113111806845603532821098673473165721600
Faltings height: 6.2395
naive height: 101.8196
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 47
regulator: 7.61164914729481556672994585203757793875517
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:12:05 UTC
last updated: 2026-09-26 20:12:05 UTC

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

(1901655, 80941972)
(1996783, 47742300)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-45, q=32; A=(3q-p)(p+q)^3=-309777, B=-(p+3q)(p-q)^3=23283183. 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 20:12:05 UTC · history