# Properties

 Label 2.7.ad_h Base Field $\F_{7}$ Dimension $2$ $p$-rank $1$ Principally polarizable Contains a Jacobian

## Invariants

 Base field: $\F_{7}$ Dimension: $2$ Weil polynomial: $1 - 3 x + 7 x^{2} - 21 x^{3} + 49 x^{4}$ Frobenius angles: $\pm0.171557865674$, $\pm0.594085680913$ Angle rank: $2$ (numerical) Number field: 4.0.28749.1 Galois group: $D_4$

This isogeny class is simple.

## Newton polygon

 $p$-rank: $1$ Slopes: $[0, 1/2, 1/2, 1]$

## Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 33 2673 108999 5808429 290838768 13905547425 678116146587 33263484668469 1628580369069621 79776985647414528

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 5 55 317 2419 17300 118195 823415 5770099 40357739 282421150

## Decomposition

This is a simple isogeny class.

## Base change

This is a primitive isogeny class.