Properties

Label 3.9.am_cq_ajl
Base Field $\F_{3^2}$
Dimension $3$
$p$-rank $3$
Does not contain a Jacobian

Learn more about

Invariants

Base field:  $\F_{3^2}$
Dimension:  $3$
Weil polynomial:  $1 - 12 x + 68 x^{2} - 245 x^{3} + 612 x^{4} - 972 x^{5} + 729 x^{6}$
Frobenius angles:  $\pm0.102429520258$, $\pm0.148726318999$, $\pm0.449329772038$
Angle rank:  $3$ (numerical)
Number field:  6.0.2216123.1
Galois group:  The Galois group of this isogeny class is not in the database.

This isogeny class is simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 181 477659 380512861 277031233843 205922569799981 150868021825933139 109671350563053918533 79799952786411184299427 58152486304039816220711488 42392617135161655297715973739

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 74 715 6434 59058 534173 4793990 43064802 387438808 3486904394

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.