# Properties

 Label 2.625.adu_fkl 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: $( 1 - 49 x + 625 x^{2} )^{2}$ Frobenius angles: $\pm0.0637685608585$, $\pm0.0637685608585$ Angle rank: $1$ (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 $A(\F_{q^r})$ 332929 151690775625 59592060966981904 23282898487386511055625 9094945010197654878745852129 3552713657817541093814153379840000 1387778780628962625902609352984947641729 542101086243205216571805161996168304364175625 211758236813626185185908677694533192411001024850704 82718061255304221841869813267320554378529632778810015625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 528 388324 244089078 152586803524 95367410590128 59604644423354974 37252902980525954928 23283064365406419073924 14551915228370363400683478 9094947017729442287143929124

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
 The isogeny class factors as 1.625.abx 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-11})$$$)$
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.a_absh $2$ (not in LMFDB) 2.625.du_fkl $2$ (not in LMFDB) 2.625.bx_cqi $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.625.a_absh $2$ (not in LMFDB) 2.625.du_fkl $2$ (not in LMFDB) 2.625.bx_cqi $3$ (not in LMFDB) 2.625.a_bsh $4$ (not in LMFDB) 2.625.abx_cqi $6$ (not in LMFDB)