Properties

Label 2.7.ad_m
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:  $1 - 3 x + 12 x^{2} - 21 x^{3} + 49 x^{4}$
Frobenius angles:  $\pm0.264975166102$, $\pm0.533843891264$
Angle rank:  $2$ (numerical)
Number field:  4.0.122536.2
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
$A(\F_{q^r})$ 38 3268 124184 5777824 287014418 13883771200 675872211122 33188953509504 1628651153229176 79801186267523428

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 65 362 2409 17075 118010 820685 5757169 40359494 282506825

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.