Properties

Label 2.13.ah_bf
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:  $1 - 7 x + 31 x^{2} - 91 x^{3} + 169 x^{4}$
Frobenius angles:  $\pm0.171237405357$, $\pm0.464284369344$
Angle rank:  $2$ (numerical)
Number field:  4.0.589541.1
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
$A(\F_{q^r})$ 103 30797 4908259 812332469 138024863248 23335821681341 3938886321816451 665406078106775525 112453276162713512311 19004944842626077700352

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 183 2233 28443 371742 4834623 62772577 815717811 10604298439 137858354518

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.