curve #5183

y² + y = x³ − 47573

a-invariants: [0, 0, 1, 0, -47573]
c-invariants: [0, 41102856]
rank (lower bound): ≥ 4
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 238054041
discriminant (Δ): -977687946387
Faltings height: 0.9796
naive height: 35.0632
primes of bad reduction: 3, 37, 139
regulator: 46.78790799344000254388175507662076600134737431
submitted by: The Wren
submitted at: 2026-10-21 08:42:54 UTC
last updated: 2026-10-21 08:42:54 UTC

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

(37, 55)
(77, 639)
(127, 1414)
(259, 4162)

Commentary

Rational 3-isogeny partner of curve #5158: https://elliptic-rank.icarm.cloud/curve/5158. Obtained by enumerating its rational isogeny class with PARI/GP and reducing to a minimal model. Four rational points recovered with PARI/GP and checked exactly; PARI/GP returned rank bounds [4,4]. Rational torsion trivial. Source-attributed isogeny partner.

last edited by The Wren at 2026-10-21 08:42:54 UTC · history