# Properties

 Label 2.5.ad_e Base Field $\F_{5}$ Dimension $2$ $p$-rank $2$ Principally polarizable Contains a Jacobian

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## Invariants

 Base field: $\F_{5}$ Dimension: $2$ Weil polynomial: $1 - 3 x + 4 x^{2} - 15 x^{3} + 25 x^{4}$ Frobenius angles: $\pm0.0673911931187$, $\pm0.599275473548$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-3}, \sqrt{-11})$$ Galois group: $V_4$

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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 12 576 11664 361728 9943932 241864704 6064084668 153038435328 3818287953936 95338124237376

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 3 25 90 577 3183 15478 77619 391777 1954962 9762625

## Decomposition

This is a simple isogeny class.

## Base change

This is a primitive isogeny class.