# Properties

 Label 2.625.ads_fgo 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: $( 1 - 25 x )^{2}( 1 - 46 x + 625 x^{2} )$ Frobenius angles: $0$, $0$, $\pm0.128188433698$ 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 $A(\F_{q^r})$ 334080 151763189760 59594309672567040 23282949931463587921920 9094945953144959085213446400 3552713671475126028465738890772480 1387778780757989861339566093792094972160 542101086242729415562632792537803191159357440 211758236813562392174376399740850992152295496280320 82718061255302130586102535275755088212492586679753932800

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 530 388510 244098290 152587140670 95367420477650 59604644652491230 37252902983989503410 23283064365385983576190 14551915228365979578311570 9094947017729212351140651550

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
 The isogeny class factors as 1.625.aby $\times$ 1.625.abu 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.abu : $$\Q(\sqrt{-6})$$.
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.ae_abok $2$ (not in LMFDB) 2.625.e_abok $2$ (not in LMFDB) 2.625.ds_fgo $2$ (not in LMFDB) 2.625.av_dw $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.625.ae_abok $2$ (not in LMFDB) 2.625.e_abok $2$ (not in LMFDB) 2.625.ds_fgo $2$ (not in LMFDB) 2.625.av_dw $3$ (not in LMFDB) 2.625.act_doi $6$ (not in LMFDB) 2.625.v_dw $6$ (not in LMFDB) 2.625.ct_doi $6$ (not in LMFDB)