Properties

Label 2.13.ak_by
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:  $( 1 - 6 x + 13 x^{2} )( 1 - 4 x + 13 x^{2} )$
Frobenius angles:  $\pm0.187167041811$, $\pm0.312832958189$
Angle rank:  $1$ (numerical)

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
$A(\F_{q^r})$ 80 28800 5074640 829440000 138211672400 23298078211200 3937112223300560 665417390653440000 112456038027485859920 19004963774689959120000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 170 2308 29038 372244 4826810 62744308 815731678 10604558884 137858491850

Decomposition

1.13.ag $\times$ 1.13.ae

Base change

This is a primitive isogeny class.