Properties

Label 2.3.ac_c
Base Field $\F_{3}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

Learn more about

Invariants

Base field:  $\F_{3}$
Dimension:  $2$
Weil polynomial:  $1-2x+2x^{2}-6x^{3}+9x^{4}$
Frobenius angles:  $\pm0.116139763599$, $\pm0.616139763599$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(i, \sqrt{5})\)
Galois group:  $V_4$

This isogeny class is simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4 80 436 6400 69044 531920 4840196 45158400 392133604 3486722000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 10 14 78 282 730 2214 6878 19922 59050

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.