curve #4343

y² + y = x³ + x² − 33713960083186166750x + 75345108757938319460479220054

a-invariants: [0, 1, 1, -33713960083186166750, 75345108757938319460479220054]
c-invariants: [1618270083992936004016, -65098173976568328517811662150936]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/5ℤ
conductor (N): 13859596811956882935
discriminant (Δ): 86984441149064392654528126085615920864445696900468503125
Faltings height: 9.8531
naive height: 146.5069
primes of bad reduction: 3, 5, 13, 17, 19, 31, 47, 83, 821, 2216321
regulator: 27569.966276878629048487476101401266165327173423460
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:05:35 UTC
last updated: 2026-10-17 10:05:35 UTC

(2883502656, 45890637994642)
(3307059841, 4377680144662)
(-8844477786371/1444, 12520093135593184889/54872)
(-286227873641/49, -92649926139163259/343)
(160501675534/49, 2600417264212291/343)
(13295006389/4, -20927523083029/8)

BASE torsion/torsion_Z5.tsv.gz:2088 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:05:36 UTC · history