Properties

Label 2.7.ae_r
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:  $( 1 - 3 x + 7 x^{2} )( 1 - x + 7 x^{2} )$
Frobenius angles:  $\pm0.308124534521$, $\pm0.439481140838$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 35 3465 138320 5769225 278414675 13803229440 678356962115 33228526386825 1628293788190160 79798373057766825

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 68 400 2404 16564 117326 823708 5764036 40350640 282496868

Decomposition

1.7.ad $\times$ 1.7.ab

Base change

This is a primitive isogeny class.