# Properties

 Label 2.625.ads_fgr 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: $( 1 - 49 x + 625 x^{2} )( 1 - 47 x + 625 x^{2} )$ Frobenius angles: $\pm0.0637685608585$, $\pm0.110824686604$ Angle rank: $2$ (numerical)

This isogeny class is not 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 $A(\F_{q^r})$ 334083 151765554825 59594520668230656 23282960303572558079625 9094946329152167820319683363 3552713682724645512448755341721600 1387778781051712755653597224556698107651 542101086249637967482328403306438358193711625 211758236813711653638273301774652237911398524679168 82718061255305130044068492484991407354309930550893591625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 530 388516 244099154 152587208644 95367424420370 59604644841226846 37252902991874067314 23283064365682703621764 14551915228376236748007410 9094947017729542145031711076

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
 The isogeny class factors as 1.625.abx $\times$ 1.625.abv and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ac_abon $2$ (not in LMFDB) 2.625.c_abon $2$ (not in LMFDB) 2.625.ds_fgr $2$ (not in LMFDB)