# Properties

 Label 1.625.abx Base Field $\F_{5^{4}}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{5^{4}}$ Dimension: $1$ L-polynomial: $1 - 49 x + 625 x^{2}$ Frobenius angles: $\pm0.0637685608585$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-11})$$ Galois group: $C_2$

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 a Jacobian, and hence is principally polarizable.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 577 389475 244114852 152587347075 95367421115377 59604644599372800 37252902982572547777 23283064365396690982275 14551915228368607603662052 9094947017729362333147159875

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 577 389475 244114852 152587347075 95367421115377 59604644599372800 37252902982572547777 23283064365396690982275 14551915228368607603662052 9094947017729362333147159875

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-11})$$.
All geometric endomorphisms are defined over $\F_{5^{4}}$.

## Base change

This is a primitive isogeny class.

## Twists

Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 1.625.bx $2$ (not in LMFDB)