Properties

Label 2.13.ah_ba
Base Field $\F_{13}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Contains a Jacobian

Learn more about

Invariants

Base field:  $\F_{13}$
Dimension:  $2$
Weil polynomial:  $( 1 - 7 x + 13 x^{2} )( 1 + 13 x^{2} )$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.5$
Angle rank:  $1$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 98 28812 4677344 800743104 137700691898 23316859190016 3937502572968986 665386850963116800 112456662227757292256 19005143383543652756652

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 173 2128 28033 370867 4830698 62750527 815694241 10604617744 137859794693

Decomposition

1.13.ah $\times$ 1.13.a

Base change

This is a primitive isogeny class.