Properties

Label 3.13.aq_em_atu
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:  $( 1 - 2 x + 13 x^{2} )( 1 - 7 x + 13 x^{2} )^{2}$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.0772104791556$, $\pm0.410543812489$
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
$A(\F_{q^r})$ 588 4148928 10270374912 22872426022656 50903316619445388 112420114045738942464 247137906022586923887228 542852069559639764582956032 1192546604047795506691655814144 2620003593342085758683201818392768

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 146 2128 28034 369238 4825292 62767150 815807810 10604617744 137858910146

Decomposition

1.13.ah 2 $\times$ 1.13.ac

Base change

This is a primitive isogeny class.