Properties

Label 2.13.am_ck
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:  $( 1 - 6 x + 13 x^{2} )^{2}$
Frobenius angles:  $\pm0.187167041811$, $\pm0.187167041811$
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
$A(\F_{q^r})$ 64 25600 4910656 829440000 138747310144 23337401574400 3938493262997056 665417390653440000 112453014483578818624 19004775447137357440000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 150 2234 29038 373682 4834950 62766314 815731678 10604273762 137857125750

Decomposition

1.13.ag 2

Base change

This is a primitive isogeny class.