curve #2228

y² + xy + y = x³ − 21591641524603x + 37861433308663623506

a-invariants: [1, 0, 1, -21591641524603, 37861433308663623506]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 5605790190
discriminant (Δ): 24957153525195079200004095854727539062500
Faltings height: 6.5387
naive height: 103.7236
primes of bad reduction: 2, 3, 5, 7, 11, 13, 29, 41, 157
regulator: 4.139714852407061272719459484596063648616
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:48:25 UTC
last updated: 2026-09-26 19:48:25 UTC

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

(2333305, 428705972)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-58, q=33; A=(3q-p)(p+q)^3=-2453125, B=-(p+3q)(p-q)^3=30896411. 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 19:48:25 UTC · history