Properties

Label 3.13.ap_ee_asn
Base Field $\F_{13}$
Dimension $3$
$p$-rank $2$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{13}$
Dimension:  $3$
Weil polynomial:  $( 1 - 7 x + 13 x^{2} )( 1 - 8 x + 39 x^{2} - 104 x^{3} + 169 x^{4} )$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.207527242884$, $\pm0.398160485086$
Angle rank:  $3$ (numerical)

Newton polygon

$p$-rank:  $2$
Slopes:  $[0, 0, 1/2, 1/2, 1, 1]$

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
$A(\F_{q^r})$ 679 4577139 10810418752 23301120712779 51125792364730699 112482149567143652352 247130633442863296681471 542827922631607749748976091 1192519411382458523679552016192 2619978482014390258241850072620379

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 161 2240 28565 370859 4827956 62765303 815771525 10604375936 137857588841

Decomposition

1.13.ah $\times$ 2.13.ai_bn

Base change

This is a primitive isogeny class.