curve #2624

y² + xy + y = x³ − x² − 458153916827x + 110970893859173579

a-invariants: [1, -1, 1, -458153916827, 110970893859173579]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 100990890
discriminant (Δ): 834933414809997970354150046784000000
Faltings height: 5.6367
naive height: 92.1650
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 59
regulator: 14.7068797624722759694616872685821057489413
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:13:26 UTC
last updated: 2026-09-26 20:13:26 UTC

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

(-718713, 263041006)
(295083, 38211898)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-39, q=20; A=(3q-p)(p+q)^3=-679041, B=-(p+3q)(p-q)^3=4312959. 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 20:13:27 UTC · history