Properties

Label 2.7.af_u
Base Field $\F_{7}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Does not contain a Jacobian

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Invariants

Base field:  $\F_{7}$
Dimension:  $2$
Weil polynomial:  $( 1 - 3 x + 7 x^{2} )( 1 - 2 x + 7 x^{2} )$
Frobenius angles:  $\pm0.308124534521$, $\pm0.376624142786$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 30 3300 143640 5940000 277894650 13714747200 677527619610 33257561040000 1628975845881720 79794405801082500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 65 414 2473 16533 116570 822699 5769073 40367538 282482825

Decomposition

1.7.ad $\times$ 1.7.ac

Base change

This is a primitive isogeny class.