Properties

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

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Invariants

Base field:  $\F_{13}$
Dimension:  $2$
Weil polynomial:  $1 - 7 x + 25 x^{2} - 91 x^{3} + 169 x^{4}$
Frobenius angles:  $\pm0.0447194275175$, $\pm0.506182643561$
Angle rank:  $2$ (numerical)
Number field:  4.0.148877.1
Galois group:  $C_4$

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
$A(\F_{q^r})$ 97 28421 4631653 798090101 137557633792 23305037451917 3936690876993517 665350440947283653 112455128083212236881 19005047316761795260416

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 171 2107 27939 370482 4828251 62737591 815649603 10604473075 137859097846

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.