curve #2402

y² + xy + y = x³ − x² − 97824973307x + 11763201693205739

a-invariants: [1, -1, 1, -97824973307, 11763201693205739]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 5986890
discriminant (Δ): 137270129095476284680858176000000
Faltings height: 5.0728
naive height: 87.5329
primes of bad reduction: 2, 3, 5, 7, 13, 17, 43
regulator: 4.944767893504102565909731418872061624855
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:59:22 UTC
last updated: 2026-09-26 19:59:22 UTC

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

(153697, 18857976)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-39, q=4; A=(3q-p)(p+q)^3=-2186625, B=-(p+3q)(p-q)^3=-2146689. 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 19:59:22 UTC · history