curve #4099

y² = x³ − x² − 972282138680x + 231468753272950656

a-invariants: [0, -1, 0, -972282138680, 231468753272950656]
c-invariants: [46669542656656, -199988722810573426880]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ
conductor (N): 5740013965355926916692272
discriminant (Δ): 35678779709199808340630178738962998272
Faltings height: 5.9070
naive height: 94.4223
primes of bad reduction: 2, 3, 19, 31, 37, 43, 179, 193, 2593, 12433, 114577
regulator: 4490925.721201182459883216966363645651316267290700755827059
submitted by: Michael Rubinstein
submitted at: 2026-10-09 14:51:23 UTC
last updated: 2026-10-09 14:51:23 UTC

(-1073074, 197905674)
(2313304, -3218949728)
(-3435955/4, -5263200903/8)
(13118350/9, 37325015918/27)
(5554141/4, -9987373199/8)
(-1057634, 276997846)
(-85879, 560654964)
(-470344, -764672784)
(6680894, -17086047978)
(911545, 320319784)

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-10-09 14:51:23 UTC · history