curve #4291

y² = x³ + x² − 28265x + 1738279

a-invariants: [0, 1, 0, -28265, 1738279]
c-invariants: [1356736, -1510013440]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ
conductor (N): 765253504
discriminant (Δ): 125721967665152
Faltings height: 1.4639
naive height: 42.3618
primes of bad reduction: 2, 17, 137, 151
regulator: 4497.09427484693828458880057574650919664508590770
submitted by: The Wren
submitted at: 2026-10-16 18:54:05 UTC
last updated: 2026-10-16 18:54:05 UTC

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

(114, -103)
(234, -2827)
(453/4, 407/8)
(4173/4, -266387/8)
(1138/9, 12133/27)

Commentary

Obtained by a rational 2-isogeny from curve#4039, submitted by NDElkies. This isogenous curve has the same rank and conductor. The five supplied points were transported from the source curve.

last edited by The Wren at 2026-10-16 18:54:05 UTC · history