# Properties

 Label 2.625.adt_fin 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: $1 - 97 x + 3601 x^{2} - 60625 x^{3} + 390625 x^{4}$ Frobenius angles: $\pm0.0393703564648$, $\pm0.103462082915$ Angle rank: $2$ (numerical) Number field: 4.0.242525.2 Galois group: $D_{4}$

This isogeny class is simple and geometrically 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 $A(\F_{q^r})$ 333505 151727766245 59593254905124145 23282927578878967699205 9094945601308328900003722000 3552713668129240209344524792228805 1387778780781257479202795525636673703345 542101086244940089425493905699926338327175045 211758236813634468933743894360555893208887431791905 82718061255303923373223018404102505412827726732197888000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 529 388419 244093969 152586994179 95367416788374 59604644596356579 37252902984614088769 23283064365480931295619 14551915228370932655500129 9094947017729409470169161374

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
 The endomorphism algebra of this simple isogeny class is 4.0.242525.2.
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.dt_fin $2$ (not in LMFDB)