# Properties

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

## Invariants

 Base field: $\F_{2^{4}}$ Dimension: $3$ L-polynomial: $( 1 - 4 x )^{2}( 1 - 10 x + 55 x^{2} - 160 x^{3} + 256 x^{4} )$ Frobenius angles: $0$, $0$, $\pm0.203888329072$, $\pm0.352056944208$ Angle rank: $2$ (numerical)

This isogeny class is not simple.

## Newton polygon

 $p$-rank: $2$ Slopes: $[0, 0, 1/2, 1/2, 1, 1]$

## 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 $A(\F_{q^r})$ 1278 15399900 69407657298 281738952914400 1151273353973692158 4719658364717363531100 19340723763427235881587138 79226803614675742178238000000 324516064130818486839763842790638 1329222780364668270507849413405497500

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 235 4139 65599 1047079 16767595 268406459 4294893631 68718949559 1099507313675

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
 The isogeny class factors as 1.16.ai $\times$ 2.16.ak_cd and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: 1.16.ai : the quaternion algebra over $$\Q$$ ramified at $2$ and $\infty$. 2.16.ak_cd : 4.0.74816.1.
All geometric endomorphisms are defined over $\F_{2^{4}}$.

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 3.16.ac_aj_eq $2$ (not in LMFDB) 3.16.c_aj_aeq $2$ (not in LMFDB) 3.16.s_fv_bdg $2$ (not in LMFDB) 3.16.ag_bf_adw $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.16.ac_aj_eq $2$ (not in LMFDB) 3.16.c_aj_aeq $2$ (not in LMFDB) 3.16.s_fv_bdg $2$ (not in LMFDB) 3.16.ag_bf_adw $3$ (not in LMFDB) 3.16.ak_ct_ami $4$ (not in LMFDB) 3.16.k_ct_mi $4$ (not in LMFDB) 3.16.ao_eh_auu $6$ (not in LMFDB) 3.16.g_bf_dw $6$ (not in LMFDB) 3.16.o_eh_uu $6$ (not in LMFDB)