# Properties

 Label 3.16.as_fy_abeb 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: $( 1 - 5 x + 16 x^{2} )( 1 - 13 x + 73 x^{2} - 208 x^{3} + 256 x^{4} )$ Frobenius angles: $\pm0.0987587980325$, $\pm0.265114785720$, $\pm0.285098958592$ Angle rank: $3$ (numerical)

This isogeny class is not 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 $A(\F_{q^r})$ 1308 15855576 71115829200 284928664614000 1154576739593228268 4720963516839107366400 19339664506865473444061268 79226291284220673300792876000 324520521294602466159155249425200 1329233950849567605986035787678097336

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 241 4238 66337 1050079 16772230 268391759 4294865857 68719893398 1099516553681

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
 The isogeny class factors as 1.16.af $\times$ 2.16.an_cv and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ai_y_abz $2$ (not in LMFDB) 3.16.i_y_bz $2$ (not in LMFDB) 3.16.s_fy_beb $2$ (not in LMFDB)