Properties

Label 3.13.aq_et_avo
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:  $( 1 - 4 x + 13 x^{2} )( 1 - 6 x + 13 x^{2} )^{2}$
Frobenius angles:  $\pm0.187167041811$, $\pm0.187167041811$, $\pm0.312832958189$
Angle rank:  $1$ (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
$A(\F_{q^r})$ 640 4608000 11245402240 23887872000000 51482189428931200 112550220068921856000 247082989636358136952960 542801726578599395328000000 1192527299149168267745577554560 2619982662302134663644776256000000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 160 2326 29276 373438 4830880 62753206 815732156 10604446078 137857808800

Decomposition

1.13.ag 2 $\times$ 1.13.ae

Base change

This is a primitive isogeny class.