Properties

Label 2.7.ae_s
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:  $( 1 - 2 x + 7 x^{2} )^{2}$
Frobenius angles:  $\pm0.376624142786$, $\pm0.376624142786$
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
$A(\F_{q^r})$ 36 3600 142884 5760000 274432356 13731152400 679467192804 33288284160000 1628762191021476 79778171970090000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 70 412 2398 16324 116710 825052 5774398 40362244 282425350

Decomposition

1.7.ac 2

Base change

This is a primitive isogeny class.