curve #2379

y² + xy = x³ − 218801714846x + 39368905525343940

a-invariants: [1, 0, 0, -218801714846, 39368905525343940]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 268772790
discriminant (Δ): 835065257722844617690710524006400
Faltings height: 5.2521
naive height: 89.9479
primes of bad reduction: 2, 3, 5, 11, 13, 31, 43, 47
regulator: 6.280158707551910528864432628455746064870
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:57:54 UTC
last updated: 2026-09-26 19:57:54 UTC

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

(222628, 41018866)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-43, q=4; A=(3q-p)(p+q)^3=-3262545, B=-(p+3q)(p-q)^3=-3218513. 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 19:57:54 UTC · history