curve #14

y² = x³ − x² − 24649x + 1355209

a-invariants: [0, -1, 0, -24649, 1355209]
c-invariants: [1183168, -1163801600]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 13217088 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 4
discriminant (Δ): 174691415199744 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 4
Faltings height: 1.4676 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 4
naive height: 41.9511 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 4
primes of bad reduction: 2, 3, 23, 41, 73
regulator: 24.11485382784266345603218697563936280642992865
submitted by: David Renshaw
submitted at: 2026-05-27 22:11:58 UTC
last updated: 2026-07-01 23:03:10 UTC

Found by Wiman (1945). A curve of rank exactly 4, via Dujella's elliptic-curve rank-records tables.

last edited by David Renshaw at 2026-05-27 22:31:46 UTC · history