# Properties

 Label 1.25.g 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: $1 + 6 x + 25 x^{2}$ Frobenius angles: $\pm0.704832764699$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-1})$$ Galois group: $C_2$ Jacobians: 4

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 4 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 32 640 15392 391680 9765152 244117120 6103668512 152587560960 3814695421472 95367450947200

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 32 640 15392 391680 9765152 244117120 6103668512 152587560960 3814695421472 95367450947200

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{2}}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-1})$$.
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.ac $\F_{5}$ 1.5.c

## Twists

Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 1.25.ag $2$ 1.625.o 1.25.ai $4$ (not in LMFDB) 1.25.i $4$ (not in LMFDB)