curve #2919

y² = x³ + x² + 87132880x + 6865805892004

a-invariants: [0, 1, 0, 87132880, 6865805892004]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 48324055603376
discriminant (Δ): -20406338818348890733884587008
Faltings height: 4.1113
naive height: 72.6383
primes of bad reduction: 2, 7, 29, 37, 71, 109, 223, 233
regulator: 1834.374918007137707898876096545034697833746457176740
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:28:22 UTC
last updated: 2026-09-26 20:28:22 UTC

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

(-16113, 1130794)
(32481/64, 1345903601/512)
(3189274/81, 6157307492/729)
(249706/9, 149459156/27)
(778318/9, -694256752/27)
(106986, -35224444)
(2535135/49, -4198990214/343)

Commentary

2-isogenous to curve#1330 via the rational 2-torsion point x=34963. 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 20:28:22 UTC · history