curve #2194

y² + xy + y = x³ − 138920772686029x + 629670797059743745556

a-invariants: [1, 0, 1, -138920772686029, 629670797059743745556]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 2874451290
discriminant (Δ): 304217937162420208104061825062626075062500
Faltings height: 6.8781
naive height: 109.3084
primes of bad reduction: 2, 3, 5, 17, 19, 29, 53, 193
regulator: 8.448304962819542793106051473873946606858
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:46:17 UTC
last updated: 2026-09-26 19:46:17 UTC

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

(-13603451, 1456419128)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-34, q=53; A=(3q-p)(p+q)^3=1323787, B=-(p+3q)(p-q)^3=82312875. 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 19:46:17 UTC · history