curve #2614

y² + xy + y = x³ − 1923683496754x + 1026099011833789556

a-invariants: [1, 0, 1, -1923683496754, 1026099011833789556]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 1434583590
discriminant (Δ): 753025926441968677721998863160736400
Faltings height: 5.8056
naive height: 96.4694
primes of bad reduction: 2, 3, 5, 11, 17, 31, 73, 113
regulator: 21.5589025909812179858032570387355707500819
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:12:50 UTC
last updated: 2026-09-26 20:12:50 UTC

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

(760069, 54960173)
(834748, 43901543)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-20, q=31; A=(3q-p)(p+q)^3=150403, B=-(p+3q)(p-q)^3=9683523. 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 20:12:50 UTC · history