Properties

Label 2.13.ao_cx
Base Field $\F_{13}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Does not contain a Jacobian

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Invariants

Base field:  $\F_{13}$
Dimension:  $2$
Weil polynomial:  $( 1 - 7 x + 13 x^{2} )^{2}$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.0772104791556$
Angle rank:  $1$ (numerical)

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 49 21609 4528384 804913641 137542331689 23293210300416 3937628638777729 665450286236357769 112457917496359649536 19005118247840541139449

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 124 2058 28180 370440 4825798 62752536 815772004 10604736114 137859612364

Decomposition

1.13.ah 2

Base change

This is a primitive isogeny class.