Properties

Label 3.13.ar_ff_axy
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:  $( 1 - 5 x + 13 x^{2} )( 1 - 6 x + 13 x^{2} )^{2}$
Frobenius angles:  $\pm0.187167041811$, $\pm0.187167041811$, $\pm0.256122854178$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 576 4377600 11137367808 23969986560000 51623572937967936 112633394568133017600 247084970698469424472128 542763847693636448256000000 1192494610632200094153107018496 2619972379027192747539176403840000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 151 2304 29375 374457 4834444 62753709 815675231 10604155392 137857267711

Decomposition

1.13.ag 2 $\times$ 1.13.af

Base change

This is a primitive isogeny class.