Properties

Label 3.13.ar_fc_axf
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:  $( 1 - 7 x + 13 x^{2} )( 1 - 10 x + 49 x^{2} - 130 x^{3} + 169 x^{4} )$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.151058869957$, $\pm0.334339837461$
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
$A(\F_{q^r})$ 553 4169067 10652248768 23367257826171 51161662525287013 112439219264720538624 247103825522123129583457 542864486380853702327156475 1192579648654060719694371545536 2620012488495518196392536516765347

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 145 2208 28645 371117 4826116 62758497 815826469 10604911584 137859378185

Decomposition

1.13.ah $\times$ 2.13.ak_bx

Base change

This is a primitive isogeny class.