curve #2825

y² + xy = x³ − 11181845072095618101356644660230x + 14391914697117329050689039214352461501292556900

a-invariants: [1, 0, 0, -11181845072095618101356644660230, 14391914697117329050689039214352461501292556900]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/7ℤ
conductor (N): 24793869011550390621870
discriminant (Δ): -105742529383568800503063422492036847927767530545199958403226680613448816451555164160000000
Faltings height: 16.3971
naive height: 226.0891
primes of bad reduction: 2, 3, 5, 7, 11, 13, 31, 43, 107, 113, 40739, 1257437
regulator: 83685.4050946712070857534543859067117171411212021
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:24:07 UTC
last updated: 2026-09-26 20:24:07 UTC

(-50212338713940, -122283501274174214105430)
(1494991187264172, 31881939944292796642986)
(1933393961761860, 230632595187600474570)
(2937317706484836, 83005881436952963158602)
(469571691228966885/16, 319772096187718923698671605/64)

Eroshkin (2009). Source: https://dujella.github.io/tors/z7old5.html (curve entry 6). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:24:07 UTC · history