curve #2290

y² + xy + y = x³ − 1878223871814x + 978934733313344536

a-invariants: [1, 0, 1, -1878223871814, 978934733313344536]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 74966430
discriminant (Δ): 10063417219243746988382558529456902400
Faltings height: 5.9061
naive height: 96.3976
primes of bad reduction: 2, 3, 5, 7, 11, 17, 23, 83
regulator: 3.459749333444739059439079508014633557087
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:52:22 UTC
last updated: 2026-09-26 19:52:22 UTC

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

(-1569307, 249128133)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-16, q=33; A=(3q-p)(p+q)^3=564995, B=-(p+3q)(p-q)^3=9764867. 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 19:52:22 UTC · history