Properties

Label 3.13.av_he_abif
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:  $( 1 - 7 x + 13 x^{2} )^{3}$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.0772104791556$, $\pm0.0772104791556$
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
$A(\F_{q^r})$ 343 3176523 9636401152 22836204908811 51009911926504363 112420114045738942464 247088272213595130613183 542841978006048990217389147 1192573227335183594875086966784 2620027586828745701170376844269043

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -7 101 1988 27989 370013 4825292 62754545 815792645 10604854484 137860172621

Decomposition

1.13.ah 3

Base change

This is a primitive isogeny class.