curve #1093

y² + xy = x³ − 304241169811532712979315990x + 2065986446448965089594679105215890328100

a-invariants: [1, 0, 0, -304241169811532712979315990, 2065986446448965089594679105215890328100]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/8ℤ
conductor (N): 3985472961137327010 ☆ record for ℤ/8ℤ torsion, rank ≥ 5
discriminant (Δ): -41577220650820854664016668523932516847644468700324001340379358523825281600000000 ☆ record for ℤ/8ℤ torsion, rank ≥ 5
Faltings height: 14.0852 ☆ record for ℤ/8ℤ torsion, rank ≥ 5
naive height: 194.5760 ☆ record for ℤ/8ℤ torsion, rank ≥ 5
primes of bad reduction: 2, 3, 5, 13, 17, 29, 31, 43, 173, 257, 367, 953
regulator: 76517.6229553013329380906072791925097957014953802
submitted by: dujella
submitted at: 2026-09-23 18:35:27 UTC
last updated: 2026-09-23 18:35:27 UTC

(10070073195332, 4839954434963286146)
(9371130643052, 6152839124497660826)
(9726832852580, 5191480617042218210)
(12667127971346, 15641060126117318462)
(63419650125532, 487696851536311240522)

found by Dujella - Lecacheux (2003)

last edited by dujella at 2026-09-23 18:35:27 UTC · history