Properties

Label 3.13.ap_ec_asa
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:  $( 1 - 6 x + 13 x^{2} )( 1 - 9 x + 39 x^{2} - 117 x^{3} + 169 x^{4} )$
Frobenius angles:  $\pm0.0228181011636$, $\pm0.187167041811$, $\pm0.419357734967$
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
$A(\F_{q^r})$ 664 4448800 10561329688 23082598800000 51032755706679424 112462364596385658400 247105977030290283831064 542785897319708794766400000 1192484527556516436306268638616 2619960440627607501302888350720000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 157 2189 28297 370184 4827109 62759045 815708369 10604065727 137856639532

Decomposition

1.13.ag $\times$ 2.13.aj_bn

Base change

This is a primitive isogeny class.