Properties

Label 2.7.af_o
Base Field $\F_{7}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{7}$
Dimension:  $2$
Weil polynomial:  $( 1 - 5 x + 7 x^{2} )( 1 + 7 x^{2} )$
Frobenius angles:  $\pm0.106147807505$, $\pm0.5$
Angle rank:  $1$ (numerical)

Newton polygon

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

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 24 2496 111456 5481216 282929064 13956074496 679258267656 33229872000000 1628921327006304 79811081670530496

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 53 324 2281 16833 118622 824799 5764273 40366188 282541853

Decomposition

1.7.af $\times$ 1.7.a

Base change

This is a primitive isogeny class.