Properties

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

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Invariants

Base field:  $\F_{7}$
Dimension:  $2$
Weil polynomial:  $( 1 - 5 x + 7 x^{2} )( 1 - x + 7 x^{2} )$
Frobenius angles:  $\pm0.106147807505$, $\pm0.439481140838$
Angle rank:  $1$ (numerical)

Newton polygon

This isogeny class is ordinary.

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

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
$A(\F_{q^r})$ 21 2457 117936 5545449 279377301 13908900096 680712388293 33256196289225 1628413520361264 79798504121221977

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 52 344 2308 16622 118222 826562 5768836 40353608 282497332

Decomposition

1.7.af $\times$ 1.7.ab

Base change

This is a primitive isogeny class.