# Properties

 Label 1.25.j Base Field $\F_{5^{2}}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{5^{2}}$ Dimension: $1$ L-polynomial: $1 + 9 x + 25 x^{2}$ Frobenius angles: $\pm0.856433706871$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-19})$$ Galois group: $C_2$ Jacobians: 1

This isogeny class is simple and geometrically simple.

## Newton polygon

This isogeny class is ordinary.

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

## Point counts

This isogeny class contains the Jacobians of 1 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 35 595 15680 390915 9761675 244168960 6103359395 152588588355 3814694891840 95367435561475

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 35 595 15680 390915 9761675 244168960 6103359395 152588588355 3814694891840 95367435561475

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{2}}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-19})$$.
All geometric endomorphisms are defined over $\F_{5^{2}}$.

## Base change

This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of $\F_{5^{2}}$.

 Subfield Primitive Model $\F_{5}$ 1.5.ab $\F_{5}$ 1.5.b

## Twists

Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 1.25.aj $2$ 1.625.abf