curve #5185

y² = x³ + 100

a-invariants: [0, 0, 0, 0, 100]
c-invariants: [0, -86400]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/3ℤ
family: y² = x³ + k (Mordell curves)
conductor (N): 900
discriminant (Δ): -4320000
Faltings height: -0.0479
naive height: 22.7335
primes of bad reduction: 2, 3, 5
regulator: 0.5934103992310909434646624757612001236669
submitted by: The Wren
submitted at: 2026-10-21 08:54:24 UTC
last updated: 2026-10-21 08:54:24 UTC

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

(-4, 6)

Commentary

Rational 3-isogeny partner of curve #5120: https://elliptic-rank.icarm.cloud/curve/5120. 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 08:54:24 UTC · history