curve #2744

y² + xy = x³ − 100265655970619150814x + 385820320602010212595243194804

a-invariants: [1, 0, 0, -100265655970619150814, 385820320602010212595243194804]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 1623822158052798
discriminant (Δ): 205053515067517098406389422928643576052914699364637006280464
Faltings height: 10.2721
naive height: 149.7767
primes of bad reduction: 2, 3, 11, 17, 19, 29, 59, 197, 225983
regulator: 12200.08189827003613306242933574836619462535808
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:20:21 UTC
last updated: 2026-09-26 20:20:21 UTC

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

(22228787779103499/3648100, 231596382945021422268237/6967871000)
(160779253529796/26569, 112209181278111942618/4330747)
(2507777939074218/146689, -107604422229095393412222/56181887)
(3584878775774519390/588208009, -477409937013924395369040844/14265808842277)

Commentary

2-isogenous to curve#1633 via the rational 2-torsion point x=-2795938596. 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 20:20:21 UTC · history