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curve #1533

y² + y = x³ − x² − 1195398x + 1558572798

a-invariants: [0, -1, 1, -1195398, 1558572798]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/5ℤ
conductor (N): 1362025 ☆ record for ℤ/5ℤ torsion, rank ≥ 3
discriminant (Δ): -939531328002055320875
Faltings height: 2.7087
naive height: 55.8567
primes of bad reduction: 5, 7, 43, 181
regulator: 24.407819133540222776437880103659682827890654
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:51:11 UTC
last updated: 2026-09-25 00:51:11 UTC

Witness: 3 independent points log in to add more points →

(-993, 42017)
(344929/25, 201994867/125)
(-524142/361, 104323622/6859)

Commentary

Torsion Z/5. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 00:51:11 UTC · history

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