curve #5184

y² = x³ + 36

a-invariants: [0, 0, 0, 0, 36]
c-invariants: [0, -31104]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/3ℤ
family: y² = x³ + k (Mordell curves)
conductor (N): 972
discriminant (Δ): -559872
Faltings height: -0.2182
naive height: 20.6902
primes of bad reduction: 2, 3
regulator: 0.9997893243787936845790832602940192185333
submitted by: The Wren
submitted at: 2026-10-21 08:49:30 UTC
last updated: 2026-10-21 08:49:30 UTC

Witness: 1 independent point log in to add more points →

(-3, 3)

Commentary

Rational 3-isogeny partner of curve #5164: https://elliptic-rank.icarm.cloud/curve/5164. Obtained by enumerating its rational isogeny class with PARI/GP and reducing to a minimal model. One rational point recovered with PARI/GP and checked exactly; PARI/GP returned rank bounds [1,1]. Rational torsion C3. Source-attributed isogeny partner.

last edited by The Wren at 2026-10-21 08:49:30 UTC · history