curve #4388

y² = x³ + x² − 113354593932583139330993260x + 355768883923009418663340824718483111908

a-invariants: [0, 1, 0, -113354593932583139330993260, 355768883923009418663340824718483111908]
c-invariants: [5441020508763990687887676496, -307384315709512783848179056500896734747456]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/6ℤ
conductor (N): 138069388263663287852601180
discriminant (Δ): 38538590878241826205631717019583799998221441048160491667032989025130486236000000
Faltings height: 13.9824
naive height: 191.5913
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 37, 41, 53, 71, 163, 173, 18913, 44417
regulator: 338665818.523454939276228765319442815138122715194070766
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:21:14 UTC
last updated: 2026-10-17 10:21:14 UTC

(-5075101991344, 28290233857861185210)
(183577405627469/4, 2424149370609203315925/8)
(101294187988609/144, 28727433291781190941975/1728)
(15593256574511, 48782133047034387000)
(8437998235876, 258702816996155070)
(8464084853211944/529, 624938668989441870714750/12167)
(736614197926266044/2209, 631888916833187549863457130/103823)
(446372166148828304/5329, 295898203879196031025002090/389017)

BASE dujella/z6old678.html#pre123 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:21:15 UTC · history