curve #3030

y² = x³ + x² + 492482975x + 26376831383679

a-invariants: [0, 1, 0, 492482975, 26376831383679]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 31226965890509248
discriminant (Δ): -308199324015416875950097235968
Faltings height: 4.3386
naive height: 75.3301
primes of bad reduction: 2, 17, 23, 31, 71, 577, 593, 1657
regulator: 77789.8089789095997941876580978352459398062760997618495
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:34:03 UTC
last updated: 2026-09-26 20:34:03 UTC

Witness: 8 independent points log in to add more points →

(-2423, 5016904)
(-18998, 3188129)
(-16406, 3725807)
(26749, 7660948)
(-7166, 4741283)
(3946, -5327441)
(5499, -5408448)
(12003361/361, -61162176544/6859)

Commentary

2-isogenous to curve#1348 via the rational 2-torsion point x=12163. 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 20:34:03 UTC · history