curve #1605

y² + y = x³ − x² − 476052030x + 4009456291878

a-invariants: [0, -1, 1, -476052030, 4009456291878]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/5ℤ
conductor (N): 2435201435 ☆ record for ℤ/5ℤ torsion, rank ≥ 4
discriminant (Δ): -39494911469628342415896875 ☆ record for ℤ/5ℤ torsion, rank ≥ 4
Faltings height: 3.7766 ☆ record for ℤ/5ℤ torsion, rank ≥ 4
naive height: 71.5624
primes of bad reduction: 5, 31, 37, 61, 6961
regulator: 332.7738371760243899767957659648736079019315338
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:27:52 UTC
last updated: 2026-09-25 01:27:52 UTC

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 01:27:52 UTC · history