curve #2928

y² + xy + y = x³ − x² − 320631239086583x − 1263501537932590302769

a-invariants: [1, -1, 1, -320631239086583, -1263501537932590302769]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 934571286991717830
discriminant (Δ): 1419926664672408870750603347523624314511360000
Faltings height: 7.3627
naive height: 111.8175
primes of bad reduction: 2, 3, 5, 7, 13, 23, 37, 47, 59, 61, 601, 1319
regulator: 539671.6539876612388721537605945151902894191337373076
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:28:47 UTC
last updated: 2026-09-26 20:28:47 UTC

Witness: 7 independent points log in to add more points →

(-9599405, -30487756898)
(-799081805/81, -22341023805842/729)
(-9621833901/625, 76561704922318/15625)
(-25724247305/1681, 531959906342942/68921)
(19721883, -9170942690)
(42983286555/1849, -4931450853903686/79507)
(63600709970971/1125721, -479224106231258809498/1194389981)

Commentary

2-isogenous to curve#2086 via the rational 2-torsion point x=123646443/4. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.

last edited by Natanael Wildner Fraga at 2026-09-26 20:28:47 UTC · history