# Properties

 Label 3.16.as_ft_abcq 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: $( 1 - 4 x )^{2}( 1 - 7 x + 16 x^{2} )( 1 - 3 x + 16 x^{2} )$ Frobenius angles: $0$, $0$, $\pm0.160861246510$, $\pm0.377642706461$ 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 $A(\F_{q^r})$ 1260 15120000 68406746940 280166402880000 1150395290605291500 4720805152607915280000 19343659154620653400550940 79229657678272771737150720000 324517256439938287898447756326860 1329222676876905031671328436250000000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 231 4079 65231 1046279 16771671 268447199 4295048351 68719202039 1099507228071

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
 The isogeny class factors as 1.16.ai $\times$ 1.16.ah $\times$ 1.16.ad 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 $\infty$. 1.16.ah : $$\Q(\sqrt{-15})$$. 1.16.ad : $$\Q(\sqrt{-55})$$.
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.am_ch_aii $2$ (not in LMFDB) 3.16.ae_af_bo $2$ (not in LMFDB) 3.16.ac_al_ea $2$ (not in LMFDB) 3.16.c_al_aea $2$ (not in LMFDB) 3.16.e_af_abo $2$ (not in LMFDB) 3.16.m_ch_ii $2$ (not in LMFDB) 3.16.s_ft_bcq $2$ (not in LMFDB) 3.16.ag_bd_aee $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.16.am_ch_aii $2$ (not in LMFDB) 3.16.ae_af_bo $2$ (not in LMFDB) 3.16.ac_al_ea $2$ (not in LMFDB) 3.16.c_al_aea $2$ (not in LMFDB) 3.16.e_af_abo $2$ (not in LMFDB) 3.16.m_ch_ii $2$ (not in LMFDB) 3.16.s_ft_bcq $2$ (not in LMFDB) 3.16.ag_bd_aee $3$ (not in LMFDB) 3.16.ak_cr_ami $4$ (not in LMFDB) 3.16.ae_bb_aey $4$ (not in LMFDB) 3.16.e_bb_ey $4$ (not in LMFDB) 3.16.k_cr_mi $4$ (not in LMFDB) 3.16.ao_ef_aum $6$ (not in LMFDB) 3.16.ai_br_agq $6$ (not in LMFDB) 3.16.a_l_adg $6$ (not in LMFDB) 3.16.a_l_dg $6$ (not in LMFDB) 3.16.g_bd_ee $6$ (not in LMFDB) 3.16.i_br_gq $6$ (not in LMFDB) 3.16.o_ef_um $6$ (not in LMFDB)