# Properties

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

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## Invariants

 Base field: $\F_{2^{4}}$ Dimension: $3$ L-polynomial: $( 1 - 7 x + 16 x^{2} )( 1 - 11 x + 61 x^{2} - 176 x^{3} + 256 x^{4} )$ Frobenius angles: $\pm0.160861246510$, $\pm0.189901625224$, $\pm0.315486115946$ 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 $A(\F_{q^r})$ 1310 15877200 71247211040 285561508144800 1156447080670947750 4724569989308567116800 19344325050557845649323790 79229698519641229741356667200 324519613489855317296518828096160 1329226979735629708856794148906250000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 241 4244 66481 1051779 16785046 268456439 4295050561 68719701164 1099510787321

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
 The isogeny class factors as 1.16.ah $\times$ 2.16.al_cj 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.ae_a_cx $2$ (not in LMFDB) 3.16.e_a_acx $2$ (not in LMFDB) 3.16.s_fy_bdz $2$ (not in LMFDB)