# Properties

 Label 3.25.d_o_gx Base field $\F_{5^{2}}$ Dimension $3$ $p$-rank $3$ Ordinary yes Supersingular no Simple yes Geometrically simple yes Primitive yes Principally polarizable yes

# Related objects

## Invariants

 Base field: $\F_{5^{2}}$ Dimension: $3$ L-polynomial: $1 + 3 x + 14 x^{2} + 179 x^{3} + 350 x^{4} + 1875 x^{5} + 15625 x^{6}$ Frobenius angles: $\pm0.289122521128$, $\pm0.484425495063$, $\pm0.914320774425$ Angle rank: $3$ (numerical) Number field: 6.0.1843390267595696.1 Galois group: $S_4\times C_2$

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable.

## Newton polygon

This isogeny class is ordinary.

 $p$-rank: $3$ Slopes: $[0, 0, 0, 1, 1, 1]$

## Point counts

This isogeny class is principally polarizable, but it is unknown whether it contains a Jacobian.

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $18047$ $251448851$ $3923225202416$ $59495198225882795$ $931412770370049920327$

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $29$ $645$ $16064$ $389909$ $9766569$ $244150908$ $6103364121$ $152587165221$ $3814693893008$ $95367484869845$

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{2}}$
 The endomorphism algebra of this simple isogeny class is 6.0.1843390267595696.1.
All geometric endomorphisms are defined over $\F_{5^{2}}$.

## Base change

This is a primitive isogeny class.

## Twists

Below is a list of all twists of this isogeny class.
TwistExtension degreeCommon base change
3.25.ad_o_agx$2$(not in LMFDB)