curve #2516

y² + xy = x³ − x² − 221146605x + 1265831924625

a-invariants: [1, -1, 0, -221146605, 1265831924625]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 203490
discriminant (Δ): 36507429211007057732100
Faltings height: 3.4270
naive height: 69.2566
primes of bad reduction: 2, 3, 5, 7, 17, 19
regulator: 6.805983583236800196099032688302329452879
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:06:27 UTC
last updated: 2026-09-26 20:06:27 UTC

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

(31365, 5002740)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-18, q=1; A=(3q-p)(p+q)^3=-103173, B=-(p+3q)(p-q)^3=-102885. 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 20:06:27 UTC · history