curve #26

y² = x³ − x² − 1485019900716x + 658252007072023716

a-invariants: [0, -1, 0, -1485019900716, 658252007072023716]
c-invariants: [71280955234384, -568729306424497084352]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 1321186210228868621060280
discriminant (Δ): 22409547184983924741173483181203078400
Faltings height: 5.9185
naive height: 95.6930
primes of bad reduction: 2, 3, 5, 11, 13, 17, 19, 23, 29, 31, 37, 8420798017
regulator: 1031223.943702713970942638847459818408913490427960735
submitted by: David Renshaw
submitted at: 2026-05-27 22:12:07 UTC
last updated: 2026-07-01 22:58:18 UTC

(-1277354, 686274900)
(2096456, 2599838590)
(6341180, 15691521794)
(5118316, 11275759890)
(7761138, 21368830956)
(6659304/25, 66330632742/125)
(206059216/25, 2927181185214/125)

Found by Penney - Pomerance (1975). A curve of rank exactly 7, via Dujella's elliptic-curve rank-records tables.

last edited by David Renshaw at 2026-05-27 22:31:58 UTC · history