Properties

Label 3.13.at_gc_abcl
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:  $( 1 - 5 x + 13 x^{2} )( 1 - 7 x + 13 x^{2} )^{2}$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.0772104791556$, $\pm0.256122854178$
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
$A(\F_{q^r})$ 441 3695139 10270374912 23261199311259 51175237809194541 112420114045738942464 247030727708668032881577 542790679774383601869692475 1192546604047795506691655814144 2620019637063803102463380377310139

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 125 2128 28517 371215 4825292 62739931 815715557 10604617744 137859754325

Decomposition

1.13.ah 2 $\times$ 1.13.af

Base change

This is a primitive isogeny class.