curve #4297

y² + xy = x³ − 2872759x + 1797128144

a-invariants: [1, 0, 0, -2872759, 1797128144]
c-invariants: [137892433, -1552925555065]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 31433727
discriminant (Δ): 121732344670410283329
Faltings height: 2.6153
naive height: 56.2260
primes of bad reduction: 3, 13, 61, 73, 181
regulator: 1315.432302400853825474662425493726926924390026
submitted by: The Wren
submitted at: 2026-10-16 19:03:11 UTC
last updated: 2026-10-16 19:03:11 UTC

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

(4061, -241003)
(1712, 42704)
(11797/9, 437402/27)
(127024/9, -45149776/27)

Commentary

Obtained by a rational 2-isogeny from curve#4065, submitted by NDElkies. This isogenous curve has the same rank and conductor, with torsion subgroup Z/2 x Z/2. The four supplied points were transported from the source curve.

last edited by The Wren at 2026-10-16 19:03:12 UTC · history