Properties

Label 2.13.ai_bi
Base Field $\F_{13}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

Learn more about

Invariants

Base field:  $\F_{13}$
Dimension:  $2$
Weil polynomial:  $1 - 8 x + 34 x^{2} - 104 x^{3} + 169 x^{4}$
Frobenius angles:  $\pm0.104164352389$, $\pm0.448054596667$
Angle rank:  $2$ (numerical)
Number field:  4.0.1088.2
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
$A(\F_{q^r})$ 92 29072 4811324 805643264 137559158172 23318043275408 3938936338883708 665444746257907712 112455376305986338268 19005059019349406723472

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 174 2190 28206 370486 4830942 62773374 815765214 10604496486 137859182734

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.