curve #2751

y² = x³ + x² − 28505124889304920920x − 18412195292655974354072151900

a-invariants: [0, 1, 0, -28505124889304920920, -18412195292655974354072151900]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 572097030360240
discriminant (Δ): 1335891520482143451624482869033194995963828610727539600000000
Faltings height: 10.2289
naive height: 146.0034
primes of bad reduction: 2, 3, 5, 7, 11, 19, 107, 167, 91183
regulator: 5887.354166120761594549236770557365673020506177
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:20:40 UTC
last updated: 2026-09-26 20:20:40 UTC

Witness: 4 independent points log in to add more points →

(-4522446735165/961, 3196472277433393800/29791)
(8466656422225/576, -22876529894327847815/13824)
(2734961426291565/252004, -123336652042860053359275/126506008)
(9628078329489414600/185761, -29875103596638960163837315290/80062991)

Commentary

2-isogenous to curve#824 via the rational 2-torsion point x=9961626491. 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 20:20:40 UTC · history