Properties

Label 3.13.ar_fb_awy
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:  $( 1 - 7 x + 13 x^{2} )( 1 - 10 x + 48 x^{2} - 130 x^{3} + 169 x^{4} )$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.116678169037$, $\pm0.350288405554$
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
$A(\F_{q^r})$ 546 4104828 10506289248 23199716148336 51051603989492106 112406642500855981824 247115407244168646198834 542882604488015191311055872 1192590029730686634236253014496 2620018383061626150738019492675068

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 143 2178 28439 370317 4824716 62761437 815853695 10605003894 137859688343

Decomposition

1.13.ah $\times$ 2.13.ak_bw

Base change

This is a primitive isogeny class.