# Properties

 Label 2.625.ado_eyw Base Field $\F_{5^{4}}$ Dimension $2$ Ordinary No $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{5^{4}}$ Dimension: $2$ L-polynomial: $( 1 - 25 x )^{2}( 1 - 42 x + 625 x^{2} )$ Frobenius angles: $0$, $0$, $\pm0.182554890994$ Angle rank: $1$ (numerical)

This isogeny class is not simple.

## Newton polygon

 $p$-rank: $1$ Slopes: $[0, 1/2, 1/2, 1]$

## Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 336384 151900250112 59598153907020288 23283024052177838407680 9094946948231806682997318144 3552713677505038927677090554437632 1387778780618887762592355702943634416128 542101086236527609911526184116318549793832960 211758236813415848684579493959383319153333502779904 82718061255299552107928778299666734512092522899643031552

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 534 388862 244114038 152587626430 95367430911894 59604644753656382 37252902980255509878 23283064365119618051710 14551915228355909186373654 9094947017728928844467250302

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
 The isogeny class factors as 1.625.aby $\times$ 1.625.abq and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: 1.625.aby : the quaternion algebra over $$\Q$$ ramified at $5$ and $\infty$. 1.625.abq : $$\Q(\sqrt{-46})$$.
All geometric endomorphisms are defined over $\F_{5^{4}}$.

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.625.ai_abgs $2$ (not in LMFDB) 2.625.i_abgs $2$ (not in LMFDB) 2.625.do_eyw $2$ (not in LMFDB) 2.625.ar_hs $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.625.ai_abgs $2$ (not in LMFDB) 2.625.i_abgs $2$ (not in LMFDB) 2.625.do_eyw $2$ (not in LMFDB) 2.625.ar_hs $3$ (not in LMFDB) 2.625.acp_dkm $6$ (not in LMFDB) 2.625.r_hs $6$ (not in LMFDB) 2.625.cp_dkm $6$ (not in LMFDB)