Properties

Label 2.3.b_b
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:  $1 + x + x^{2} + 3 x^{3} + 9 x^{4}$
Frobenius angles:  $\pm0.327011428181$, $\pm0.798251144367$
Angle rank:  $2$ (numerical)
Number field:  4.0.16317.1
Galois group:  $D_{4}$

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
$A(\F_{q^r})$ 15 105 945 8925 49200 522585 4607205 43063125 397583235 3477062400

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 11 35 107 200 719 2105 6563 20195 58886

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.