curve #2886

y² + xy = x³ + 52758245125456934645x + 522160152165444318965039959025

a-invariants: [1, 0, 0, 52758245125456934645, 522160152165444318965039959025]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/6ℤ
conductor (N): 48851058662780160570
discriminant (Δ): -127183665649418728457393294997146577614890243544921731479744000
Faltings height: 10.5982
naive height: 150.3787
primes of bad reduction: 2, 3, 5, 7, 19, 23, 31, 271, 277, 367, 623299
regulator: 1707394.9859551542113914684349206640078650516876487
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:26:51 UTC
last updated: 2026-09-26 20:26:51 UTC

Witness: 6 independent points log in to add more points →

(645635300, -745984147972645)
(18302316176750/2209, 128339359613087441935/103823)
(11524890140, 1631240596362065)
(1014237515509/144, -1926675790963603189/1728)
(314140258000/169, -1739175231348277715/2197)
(13579455966080/289, 50759260257258338185/4913)

Commentary

2-isogenous to curve#1914 via the rational 2-torsion point x=2967450110. 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 20:26:51 UTC · history