curve #1692

y² = x³ − x² − 33407504x + 74332001280

a-invariants: [0, -1, 0, -33407504, 74332001280]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/4ℤ
conductor (N): 62703888
discriminant (Δ): 37422199951910572032 ☆ record for ℤ/4ℤ torsion, rank ≥ 4
Faltings height: 2.9206
naive height: 63.5865
primes of bad reduction: 2, 3, 13, 17, 23, 257
regulator: 27.52986278960443775503832395901323682199316358
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:10:58 UTC
last updated: 2026-09-25 06:10:58 UTC

Torsion Z/4. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 06:10:58 UTC · history