curve #2515

y² + xy + y = x³ − 49428958x + 130902669056

a-invariants: [1, 0, 1, -49428958, 130902669056]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 278070
discriminant (Δ): 326012490022276190250000
Faltings height: 3.2959
naive height: 64.7617
primes of bad reduction: 2, 3, 5, 13, 23, 31
regulator: 2.126481347554882323090287607257033309699
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:06:23 UTC
last updated: 2026-09-26 20:06:23 UTC

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

(-8060, 79592)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-4, q=9; A=(3q-p)(p+q)^3=3875, B=-(p+3q)(p-q)^3=50531. 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 20:06:23 UTC · history