# Properties

 Label 3.16.as_ft_abcp 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: $1 - 18 x + 149 x^{2} - 743 x^{3} + 2384 x^{4} - 4608 x^{5} + 4096 x^{6}$ Frobenius angles: $\pm0.0886101669467$, $\pm0.128503209264$, $\pm0.379739504037$ Angle rank: $3$ (numerical) Number field: 6.0.6336239.1 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 $A(\F_{q^r})$ 1261 15130739 68472134809 280482881626571 1151358791893282141 4722851778072874107389 19347054850360525691260936 79234447132012101478312875371 324523361072658382358599700786221 1329229916646326550667763441789632229

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 231 4082 65303 1047154 16778940 268494316 4295307975 68720494739 1099513216676

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
 The endomorphism algebra of this simple isogeny class is 6.0.6336239.1.
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_ft_bcp $2$ (not in LMFDB)