curve #2260

y² + xy + y = x³ − 155407254138778x + 745684167632659733756

a-invariants: [1, 0, 1, -155407254138778, 745684167632659733756]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 3463398510
discriminant (Δ): 126508486430406006381151360317332250000
Faltings height: 6.6746
naive height: 109.6448
primes of bad reduction: 2, 3, 5, 11, 13, 47, 89, 193
regulator: 4.575339168272070474855406572881728919053
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:50:24 UTC
last updated: 2026-09-26 19:50:24 UTC

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

(7201345, 8295497)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-52, q=47; A=(3q-p)(p+q)^3=-24125, B=-(p+3q)(p-q)^3=86356611. 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 19:50:24 UTC · history