Properties

Label 2.7.af_p
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:  $1 - 5 x + 15 x^{2} - 35 x^{3} + 49 x^{4}$
Frobenius angles:  $\pm0.13951984276$, $\pm0.487441680688$
Angle rank:  $2$ (numerical)
Number field:  4.0.62181.1
Galois group:  $D_4$

This isogeny class is simple.

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
$A(\F_{q^r})$ 25 2625 116575 5578125 284182000 13990748625 680123884675 33232466203125 1628591397293725 79804102912800000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 55 339 2323 16908 118915 825849 5764723 40358013 282517150

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.