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curve #4847

y² + y = x³ − 21

a-invariants: [0, 0, 1, 0, -21]
c-invariants: [0, 17928]
rank (lower bound): ≥ 2
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 186003
discriminant (Δ): -186003
Faltings height: -0.3100
naive height: 19.5882
primes of bad reduction: 3, 83
regulator: 7.23638882492954661579110214958616730224201
submitted by: Daniel Błażewicz
submitted at: 2026-10-20 22:05:12 UTC
last updated: 2026-10-20 22:05:12 UTC

Witness: 2 independent points log in to add more points →

(3, 2)
(69/25, 3/125)

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