curve #4386

y² + xy + y = x³ + x² + 15826828814078107235x − 6612014528461592389020920845

a-invariants: [1, 1, 1, 15826828814078107235, -6612014528461592389020920845]
c-invariants: [-759687783075749147279, 5712780558288474197182194214519]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/4ℤ
conductor (N): 42744841527109526140830
discriminant (Δ): -272610575488097182067608344389779043425264015438718400000000
Faltings height: 10.0937
naive height: 144.2383
primes of bad reduction: 2, 3, 5, 13, 29, 41, 59, 83, 97, 103, 337, 647, 8641
regulator: 6217040.50054608291370913418188188831740578061435743128
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:21:08 UTC
last updated: 2026-10-17 10:21:08 UTC

(74148450463, 20219620752656268)
(12806495365/16, 5186997082014831/64)
(991036579117/784, 2725411412178003261/21952)
(256819565663/121, 254430626612895468/1331)
(272022744337/49, 172300303625272374/343)
(781765755527/529, 1720863986735709756/12167)
(7404600057737/1024, 22842048561065706699/32768)
(7532945381069/1936, 28745930126024263125/85184)

BASE records/family_Z4.md#40 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:21:08 UTC · history