curve #425

y² + xy + y = x³ − x²

a-invariants: [1, -1, 1, 0, 0]
rank (lower bound): ≥ 1
torsion subgroup: trivial
conductor (N): 53
discriminant (Δ): -53
Faltings height: -0.9885
naive height: 11.3875
primes of bad reduction: 53
regulator: 0.09298148463865430334804190550967810967388
submitted by: NDElkies
submitted at: 2026-08-29 17:27:26 UTC
last updated: 2026-08-29 17:27:26 UTC

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

(0, 0)

Commentary

The third elliptic curve of positive rank (LMFDB 53.a1, also the Fricke quotient of the modular curve X_0(53)), which happens to have a somewhat smaller naive height than the rank-1 curve of conductor 37.

last edited by NDElkies at 2026-08-29 17:27:26 UTC · history