curve #2738

y² + xy = x³ − 54326064336278369814x + 50852129363364295006901630244

a-invariants: [1, 0, 0, -54326064336278369814, 50852129363364295006901630244]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 2102768214757266
discriminant (Δ): 9144229140796918280110011172769317296641959623894777201041664
Faltings height: 10.3895
naive height: 147.9382
primes of bad reduction: 2, 3, 7, 17, 19, 37, 41, 59, 137, 12641
regulator: 1029.903922724717077216793449717812597499327161
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:20:06 UTC
last updated: 2026-09-26 20:20:06 UTC

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

(43276210236990/2809, -252241862173101259164/148877)
(34880172465150/169, -205869760380962074314/2197)
(14284953644580/121, -53886201358243351698/1331)
(27921549987/4, -867582877290057/8)

Commentary

2-isogenous to curve#1636 via the rational 2-torsion point x=62402710175/4. 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 20:20:06 UTC · history