curve #4346

y² + xy + y = x³ + x² − 834833989862295955x + 854342817030819103741134225

a-invariants: [1, 1, 1, -834833989862295955, 854342817030819103741134225]
c-invariants: [40072031513390205841, -738152194215167941982766514361]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/5ℤ
conductor (N): 3984881709897028990
discriminant (Δ): -278080027524296967663860461510476692382617212613427200000
Faltings height: 9.5156
naive height: 137.5479
primes of bad reduction: 2, 5, 7, 23, 29, 43, 107, 18169, 1020959
regulator: 19074.569076074451464687607113802501021153781886371
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:05:41 UTC
last updated: 2026-10-17 10:05:41 UTC

(122779022587/9, 42932039322557306/27)
(32775759283/81, 17598659452918462/729)
(213226043, 26192046115678)
(122768608307/49, 41288979126557954/343)
(1302788853, 44472938999078)
(64916396843/121, 31521487517946218/1331)

BASE torsion/torsion_Z5.tsv.gz:2086 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:05:41 UTC · history