Properties

Label 2.7.ae_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:  $( 1 - 4 x + 7 x^{2} )( 1 + 7 x^{2} )$
Frobenius angles:  $\pm0.227185525829$, $\pm0.5$
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
$A(\F_{q^r})$ 32 3072 125216 5750784 286475552 13956074496 677806359584 33182023680000 1627906030229024 79795523624881152

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 62 364 2398 17044 118622 823036 5755966 40341028 282486782

Decomposition

1.7.ae $\times$ 1.7.a

Base change

This is a primitive isogeny class.