Properties

Label 2.13.ag_w
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:  $1 - 6 x + 22 x^{2} - 78 x^{3} + 169 x^{4}$
Frobenius angles:  $\pm0.13137925795$, $\pm0.526761541651$
Angle rank:  $2$ (numerical)
Number field:  4.0.8112.1
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
$A(\F_{q^r})$ 108 29808 4713228 807439104 138258290988 23333363095536 3937787128076364 665426158870376448 112458741497626342572 19005088576997958498288

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 8 178 2144 28270 372368 4834114 62755064 815742430 10604813816 137859397138

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.