Properties

Label 3.13.ap_dx_aqq
Base Field $\F_{13}$
Dimension $3$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{13}$
Dimension:  $3$
Weil polynomial:  $( 1 - 7 x + 13 x^{2} )( 1 - 8 x + 32 x^{2} - 104 x^{3} + 169 x^{4} )$
Frobenius angles:  $\pm0.0370621216586$, $\pm0.0772104791556$, $\pm0.462937878341$
Angle rank:  $2$ (numerical)

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 630 4154220 10012857120 22657863639600 50895254892840750 112443633371876002560 247075057715527390608630 542769149576876086635724800 1192514971681397866466643104160 2620006291359067191715284001015500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 147 2072 27767 369179 4826304 62751191 815683199 10604336456 137859052107

Decomposition

1.13.ah $\times$ 2.13.ai_bg

Base change

This is a primitive isogeny class.