# Properties

 Label 2.625.ado_eyz Base Field $\F_{5^{4}}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{5^{4}}$ Dimension: $2$ L-polynomial: $1 - 92 x + 3353 x^{2} - 57500 x^{3} + 390625 x^{4}$ Frobenius angles: $\pm0.0400093343905$, $\pm0.177873335421$ Angle rank: $2$ (numerical) Number field: 4.0.4665921.1 Galois group: $D_{4}$

This isogeny class is simple and geometrically 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 $A(\F_{q^r})$ 336387 151902613977 59598356105425968 23283033413519102437161 9094947262246318603237424067 3552713686045123824442152274608384 1387778780818104056610542627104743218787 542101086240648742000863111413101593351397833 211758236813493247349501871654776710279896062964144 82718061255300899695208571847146296575064435869964222457

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 534 388868 244114866 152587687780 95367434204574 59604644896935230 37252902985603181550 23283064365296619327172 14551915228361227982127186 9094947017729077013255607908

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
 The endomorphism algebra of this simple isogeny class is 4.0.4665921.1.
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 2.625.do_eyz $2$ (not in LMFDB)