curve #2921

y² + xy = x³ + 50627101565668207228579525x + 31560876466833383058857093536380500625

a-invariants: [1, 0, 0, 50627101565668207228579525, 31560876466833383058857093536380500625]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/5ℤ
conductor (N): 98401480189946941347452490
discriminant (Δ): -8735110210745040575633189159338404212814641711059404452828409934970703062400000
Faltings height: 13.8366
naive height: 189.1732
primes of bad reduction: 2, 3, 5, 7, 19, 23, 31, 53, 73, 167, 4139, 16691, 774901
regulator: 983427.3277015715089767112757879686903438280297491906
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:28:29 UTC
last updated: 2026-09-26 20:28:29 UTC

Witness: 7 independent points log in to add more points →

(-605169073250, -837429992429581775)
(-364576031330, -3613168901523318095)
(-235888035350, -4427801072954045975)
(1546697018650, 10656724003864614025)
(-574263218390, -1515986080954691735)
(3969736276270, 17178339680519480305)
(-367692673010, -3591093088057271375)

Commentary

Dujella - Lecacheux (2009). Source: https://dujella.github.io/tors/z5old678.html (curve entry 28). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:28:29 UTC · history