# Properties

 Label 3.16.as_fx_abdt Base Field $\F_{2^{4}}$ Dimension $3$ Ordinary Yes $p$-rank $3$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{2^{4}}$ Dimension: $3$ L-polynomial: $1 - 18 x + 153 x^{2} - 773 x^{3} + 2448 x^{4} - 4608 x^{5} + 4096 x^{6}$ Frobenius angles: $\pm0.109406132665$, $\pm0.208302636123$, $\pm0.327763380346$ Angle rank: $3$ (numerical) Number field: 6.0.53163783.1 Galois group: $A_4\times C_2$

This isogeny class is simple and geometrically simple.

## 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 does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 1299 15714003 70610588649 284197314082827 1154536315694943789 4722792817067707241133 19343451997189727152706496 79230094696154960740871111307 324521185308632713376169547190031 1329229602188956485591291918661824813

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 239 4208 66167 1050044 16778732 268444322 4295072039 68720034011 1099512956564

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
 The endomorphism algebra of this simple isogeny class is 6.0.53163783.1.
All geometric endomorphisms are defined over $\F_{2^{4}}$.

## 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 3.16.s_fx_bdt $2$ (not in LMFDB)