Properties

Label 2.7.ae_j
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:  $\pm0.106147807505$, $\pm0.560518859162$
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
$A(\F_{q^r})$ 27 2457 104976 5545449 286480827 13908900096 677804147019 33256196289225 1629429133651344 79798504121221977

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 52 304 2308 17044 118222 823036 5768836 40378768 282497332

Decomposition

1.7.af $\times$ 1.7.b

Base change

This is a primitive isogeny class.