# Properties

 Label 3.16.as_fu_abcx 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: $( 1 - 7 x + 16 x^{2} )( 1 - 11 x + 57 x^{2} - 176 x^{3} + 256 x^{4} )$ Frobenius angles: $\pm0.0728689886706$, $\pm0.160861246510$, $\pm0.368631800070$ 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 $A(\F_{q^r})$ 1270 15270480 68971993120 281276896932000 1151846432542081750 4722392578368749184000 19345656943985097319360630 79232673095668668222155592000 324521464240277940063829139426080 1329227415473205395064169597044762000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 233 4112 65489 1047599 16777310 268474919 4295211809 68720093072 1099511147753

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
 The isogeny class factors as 1.16.ah $\times$ 2.16.al_cf 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_ae_bv $2$ (not in LMFDB) 3.16.e_ae_abv $2$ (not in LMFDB) 3.16.s_fu_bcx $2$ (not in LMFDB)