Properties

Label 3.13.ap_ee_asm
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:  $( 1 - 6 x + 13 x^{2} )( 1 - 9 x + 41 x^{2} - 117 x^{3} + 169 x^{4} )$
Frobenius angles:  $\pm0.109149799241$, $\pm0.187167041811$, $\pm0.400911184348$
Angle rank:  $3$ (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
$A(\F_{q^r})$ 680 4583200 10829381480 23350945680000 51206443416310400 112568218669671623200 247196800994063115498920 542866357155795385896000000 1192536010021171371049232913320 2619982089030695746857167994880000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 161 2243 28625 371444 4831649 62782103 815829281 10604523539 137857778636

Decomposition

1.13.ag $\times$ 2.13.aj_bp

Base change

This is a primitive isogeny class.