Properties

Label 2.7.ai_be
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:  $( 1 - 4 x + 7 x^{2} )^{2}$
Frobenius angles:  $\pm0.227185525829$, $\pm0.227185525829$
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
$A(\F_{q^r})$ 16 2304 132496 6230016 290497936 13908900096 677388257296 33186447949824 1627398540096784 79779792113236224

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 46 384 2590 17280 118222 822528 5756734 40328448 282431086

Decomposition

1.7.ae 2

Base change

This is a primitive isogeny class.