curve #4261

y² + xy + y = x³ − x² − 642423119659268492x + 168015123233810528707511695

a-invariants: [1, -1, 1, -642423119659268492, 168015123233810528707511695]
c-invariants: [30836309743644887601, -145165066335248902956888110505]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/2ℤ
conductor (N): 74484734718315567875349937711158
discriminant (Δ): 4773537042427546018312798825340506294971165966329352192
Faltings height: 9.2138
naive height: 134.6257
primes of bad reduction: 2, 3, 11, 23, 61, 73, 127, 223, 827, 1583, 8663, 52177, 219169
regulator: 32400325377.4110940190444355200230959253198420149522144147200
submitted by: The Wren
submitted at: 2026-10-15 21:02:54 UTC
last updated: 2026-10-15 21:02:54 UTC

(-710416459, 16305627369781)
(-189570155, 16822306903349)
(64602929, 11259733719665)
(78601705, 10862980074509)
(279740929, 3192696757505)
(645370517, 4712744866997)
(3642408853, 214829284199477)
(19580160415/4, 2704825593676387/8)
(-4721845613/9, 512757336267263/27)
(7434606461/25, 225968480938769/125)
(98862097861/9, 31003528532499335/27)

Found by specializing the family associated with curve#802 at T = 17/3. PARI/GP returned rank bounds [11,11]. Eleven rational points are supplied.

last edited by The Wren at 2026-10-15 21:02:54 UTC · history