curve #2238

y² + xy = x³ − 108506674900366x + 435038475610151312900

a-invariants: [1, 0, 0, -108506674900366, 435038475610151312900]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 4958957190
discriminant (Δ): 1927307004305578172576828209970971545600
Faltings height: 6.6801
naive height: 108.5671
primes of bad reduction: 2, 3, 5, 11, 37, 53, 79, 97
regulator: 3.924441860596583643069825493593708236509
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:49:02 UTC
last updated: 2026-09-26 19:49:02 UTC

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

(6034076, 42923714)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-53, q=44; A=(3q-p)(p+q)^3=-134865, B=-(p+3q)(p-q)^3=72101167. 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 19:49:02 UTC · history