curve #2378

y² + xy + y = x³ − x² − 103075633247x + 3720643774088519

a-invariants: [1, -1, 1, -103075633247, 3720643774088519]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 8584290
discriminant (Δ): 64108525348908014315503878144000000
Faltings height: 5.3703
naive height: 87.6898
primes of bad reduction: 2, 3, 5, 11, 13, 23, 29
regulator: 2.641114765180300995148689829997051211328
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:57:51 UTC
last updated: 2026-09-26 19:57:51 UTC

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

(-331481, 38443122)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-39, q=16; A=(3q-p)(p+q)^3=-1058529, B=-(p+3q)(p-q)^3=1497375. 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 19:57:51 UTC · history