curve #2877

y² + xy + y = x³ − 8969476x − 3812628402

a-invariants: [1, 0, 1, -8969476, -3812628402]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 88246450450
discriminant (Δ): 39905743033221122562500
Faltings height: 3.0296
naive height: 59.6416
primes of bad reduction: 2, 5, 29, 41, 59, 139, 181
regulator: 225.18507296928700340458213295770975905213131196102
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:26:29 UTC
last updated: 2026-09-26 20:26:29 UTC

Witness: 6 independent points log in to add more points →

(-2334, 67566)
(-14282/9, 2185697/27)
(-4293/4, -536993/8)
(-2457, -57033)
(-1268, -73679)
(-15054/25, -4589421/125)

Commentary

2-isogenous to curve#1303 via the rational 2-torsion point x=1377. 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 20:26:29 UTC · history