curve #2837

y² + xy = x³ − x² − 583975053x + 66571684245

a-invariants: [1, -1, 0, -583975053, 66571684245]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 37109896434
discriminant (Δ): 12743769394987224789362163984
Faltings height: 4.0824
naive height: 72.1697
primes of bad reduction: 2, 3, 13, 23, 107, 4957
regulator: 962.136792571441803944292397587115229840318281551
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:24:41 UTC
last updated: 2026-09-26 20:24:41 UTC

Witness: 5 independent points log in to add more points →

(-232229/25, -270112896/125)
(1369923/49, -815893077/343)
(25421478/289, 123032546031/4913)
(233542, -112372993)
(45688686/1849, -68612491839/79507)

Commentary

2-isogenous to curve#1700 via the rational 2-torsion point x=193779/4. 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 20:24:41 UTC · history