# Properties

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

## Invariants

 Base field: $\F_{5^{4}}$ Dimension: $2$ L-polynomial: $( 1 - 25 x )^{2}( 1 - 47 x + 625 x^{2} )$ Frobenius angles: $0$, $0$, $\pm0.110824686604$ 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 is principally polarizable, but does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 333504 151726977792 59593183840124928 23282924033616449080320 9094945470272953332640023744 3552713664112294973059395017244672 1387778780673206929525437879489281988288 542101086242306040340621284561503887086858240 211758236813575081126396704350644278179168450985984 82718061255302668143228043611353054683575428530146269952

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 529 388417 244093678 152586970945 95367415414369 59604644528963422 37252902981713628913 23283064365367799748865 14551915228366851556454734 9094947017729271456171660577

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
 The isogeny class factors as 1.625.aby $\times$ 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: 1.625.aby : the quaternion algebra over $$\Q$$ ramified at $5$ and $\infty$. 1.625.abv : $$\Q(\sqrt{-291})$$.
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.ad_abqi $2$ (not in LMFDB) 2.625.d_abqi $2$ (not in LMFDB) 2.625.dt_fim $2$ (not in LMFDB) 2.625.aw_cx $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.625.ad_abqi $2$ (not in LMFDB) 2.625.d_abqi $2$ (not in LMFDB) 2.625.dt_fim $2$ (not in LMFDB) 2.625.aw_cx $3$ (not in LMFDB) 2.625.acu_dph $6$ (not in LMFDB) 2.625.w_cx $6$ (not in LMFDB) 2.625.cu_dph $6$ (not in LMFDB)