curve #2617

y² + xy = x³ − 2892251831910x + 1893056937877520100

a-invariants: [1, 0, 0, -2892251831910, 1893056937877520100]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 454799730
discriminant (Δ): 274786769420095092485436707904000000
Faltings height: 5.8330
naive height: 97.6928
primes of bad reduction: 2, 3, 5, 7, 11, 47, 59, 71
regulator: 9.29500133133385534929737317865868410080258
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:13:01 UTC
last updated: 2026-09-26 20:13:01 UTC

Witness: 2 independent points log in to add more points →

(-1808100, 1101563610)
(-1523508, 1663063626)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-59, q=4; A=(3q-p)(p+q)^3=-11812625, B=-(p+3q)(p-q)^3=-11752209. 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 20:13:01 UTC · history