Properties

Label 3.13.ar_fe_axt
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:  $( 1 - 7 x + 13 x^{2} )( 1 - 5 x + 13 x^{2} )^{2}$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.256122854178$, $\pm0.256122854178$
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
$A(\F_{q^r})$ 567 4298427 10946057472 23694103094571 51341099522009787 112420114045738942464 246973196605307985010863 542739386390369424398926875 1192519981354751996352349595904 2620011687322981914904984277550147

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 149 2268 29045 372417 4825292 62725317 815638469 10604381004 137859336029

Decomposition

1.13.ah $\times$ 1.13.af 2

Base change

This is a primitive isogeny class.