curve #2514

y² + xy + y = x³ − 55935204x + 151397748706

a-invariants: [1, 0, 1, -55935204, 151397748706]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 51870
discriminant (Δ): 1297852417956067777440000
Faltings height: 3.3759
naive height: 65.1327
primes of bad reduction: 2, 3, 5, 7, 13, 19
regulator: 5.755875100150346457441786253559087504384
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:06:20 UTC
last updated: 2026-09-26 20:06:20 UTC

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

(-5039, 555071)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-16, q=3; A=(3q-p)(p+q)^3=-54925, B=-(p+3q)(p-q)^3=-48013. 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 20:06:20 UTC · history