curve #5186

y² = x³ + 4

a-invariants: [0, 0, 0, 0, 4]
c-invariants: [0, -3456]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/3ℤ
family: y² = x³ + k (Mordell curves)
conductor (N): 108
discriminant (Δ): -6912
Faltings height: -0.5844
naive height: 16.2957
primes of bad reduction: 2, 3
regulator: 1
submitted by: The Wren
submitted at: 2026-10-21 08:56:11 UTC
last updated: 2026-10-21 08:56:11 UTC

Witness: no points (rank ≥ 0 needs none) log in to add more points →

Commentary

Rational 3-isogeny partner of curve #5113: https://elliptic-rank.icarm.cloud/curve/5113. Obtained by enumerating its rational isogeny class with PARI/GP. No points submitted; PARI/GP returned rank bounds [0,0]. Rational torsion C3. Source-attributed isogeny partner.

last edited by The Wren at 2026-10-21 08:56:11 UTC · history