curve #3858

y² + xy = x³ − 49968470170082985336x + 142984524647959265391126935616

a-invariants: [1, 0, 0, -49968470170082985336, 142984524647959265391126935616]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/3ℤ
conductor (N): 8076976900985252575372187130
discriminant (Δ): -847180869993815088158267375392159182841943958465502787174400
Faltings height: 10.2537
naive height: 147.7882
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 31, 61, 71, 173, 46881400253581
regulator: 344476878.14218067316936338249982834299414175580661736666
submitted by: Maksym Voznyy
submitted at: 2026-10-04 00:17:47 UTC
last updated: 2026-10-04 00:17:47 UTC

(451274107547284631536/252183748041, -30838752750241075164914077159592/126641382407481339)
(1672326411836620450434920557016/364401227464226230201, 706705434893466815152994004244766580422537888/6956162948123726811440736795949)
(43585700294842539984/6203610169, 181989208952537902837385306904/488614947740947)
(63142535874515292/316969, 15856702452464318760737700/178453547)
(33487957296, -6002057007878328)
(-6760257984, -414524217234888)
(615890204096961578353644537864/171876863499065078929, 224674796224410844733682959466507186093143304/2253336905858165650409274268217)
(-65515270462992/17161, 1185553598551901253720/2248091)
(348079190724/121, -202061530826531892/1331)

Eroshkin - Voznyy (2026)

last edited by Maksym Voznyy at 2026-10-04 00:17:47 UTC · history