curve #2348

y² + xy + y = x³ − 299091325979x − 61622238702522094

a-invariants: [1, 0, 1, -299091325979, -61622238702522094]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 37962870
discriminant (Δ): 71913220784603620143250892044522500
Faltings height: 5.4727
naive height: 90.8856
primes of bad reduction: 2, 3, 5, 11, 17, 67, 101
regulator: 8.510386354461711824023948375179005103424
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:55:59 UTC
last updated: 2026-09-26 19:55:59 UTC

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

(637428, 81686698)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-50, q=17; A=(3q-p)(p+q)^3=-3629637, B=-(p+3q)(p-q)^3=300763. 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 19:55:59 UTC · history