Properties

Label 3.13.ap_eb_ars
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:  $( 1 - 7 x + 13 x^{2} )( 1 - 8 x + 36 x^{2} - 104 x^{3} + 169 x^{4} )$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.147614849952$, $\pm0.431019279425$
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
$A(\F_{q^r})$ 658 4394124 10465874272 23043647504304 51092959908644458 112566898734816363264 247196797297426767647794 542852706140314393827225600 1192536973193493054737051483104 2619999422337770858415665380625964

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 155 2168 28247 370619 4831592 62782103 815808767 10604532104 137858690675

Decomposition

1.13.ah $\times$ 2.13.ai_bk

Base change

This is a primitive isogeny class.