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curve #1421

y² + y = x³ + x² − 1293x + 21540

a-invariants: [0, 1, 1, -1293, 21540]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/3ℤ
conductor (N): 4123
discriminant (Δ): -70087408867
Faltings height: 0.7957
naive height: 33.5181
primes of bad reduction: 7, 19, 31
regulator: 0.962450460384998281154072436516201862724206
submitted by: Michael Rubinstein
submitted at: 2026-09-24 23:31:19 UTC
last updated: 2026-09-24 23:31:19 UTC

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

(-20, 199)
(-234/25, 22614/125)

Commentary

Torsion Z/3. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 23:31:19 UTC · history

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