curve #4528

y² + y = x³ − x² − 1867256149029934720x + 1525295412556651371915773338

a-invariants: [0, -1, 1, -1867256149029934720, 1525295412556651371915773338]
c-invariants: [89628295153436866576, -1317855235911177014414606964824]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/5ℤ
conductor (N): 43068006120189154715
discriminant (Δ): -588389813387326978864865203237309464666121649761622946875
Faltings height: 9.5912
naive height: 138.7071
primes of bad reduction: 5, 13, 31, 37, 41, 107, 239, 241, 401, 5701
regulator: 152643.17777811526274252226971313066822394550928887
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:33:59 UTC
last updated: 2026-10-17 10:33:59 UTC

(5974768019, 451281799759212)
(826651339, 23379902105732)
(-1151869230226/3721, 10336131070845789897/226981)
(381287875874/121, 218426456933358847/1331)
(2592862404221/2209, 3201245374544420451/103823)
(35612218208161/12769, 193643734398349260889/1442897)

BASE torsion/torsion_Z5.tsv.gz:2100 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:34:00 UTC · history