# Properties

 Label 1.625.abq 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: $1 - 42 x + 625 x^{2}$ Frobenius angles: $\pm0.182554890994$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-46})$$ 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 $A(\F_{q^r})$ 584 390112 244145288 152588407680 95367450443144 59604645241937632 37252902992462541128 23283064365424793832960 14551915228363538580904904 9094947017729119579330531552

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 584 390112 244145288 152588407680 95367450443144 59604645241937632 37252902992462541128 23283064365424793832960 14551915228363538580904904 9094947017729119579330531552

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-46})$$.
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.bq $2$ (not in LMFDB)