# Properties

 Label 3.16.ax_iq_abto Base Field $\F_{2^{4}}$ Dimension $3$ Ordinary No $p$-rank $1$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{2^{4}}$ Dimension: $3$ L-polynomial: $( 1 - 4 x )^{4}( 1 - 7 x + 16 x^{2} )$ Frobenius angles: $0$, $0$, $0$, $0$, $\pm0.160861246510$ Angle rank: $1$ (numerical)

This isogeny class is not simple.

## Newton polygon

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

## 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 $A(\F_{q^r})$ 810 12150000 64429610490 278049761100000 1150257900970010250 4720046579850542850000 19340269237143852590462490 79224827362032043628645400000 324514006504456338488872440778410 1329222076797878890353805830468750000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -6 176 3834 64736 1046154 16768976 268400154 4294786496 68718513834 1099506731696

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
 The isogeny class factors as 1.16.ai 2 $\times$ 1.16.ah 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 2 : $\mathrm{M}_{2}(B)$, where $B$ is the quaternion algebra over $$\Q$$ ramified at $2$ and $\infty$. 1.16.ah : $$\Q(\sqrt{-15})$$.
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.aj_a_ge $2$ (not in LMFDB) 3.16.ah_aq_iq $2$ (not in LMFDB) 3.16.h_aq_aiq $2$ (not in LMFDB) 3.16.j_a_age $2$ (not in LMFDB) 3.16.x_iq_bto $2$ (not in LMFDB) 3.16.al_bs_aey $3$ (not in LMFDB) 3.16.b_i_adc $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.16.aj_a_ge $2$ (not in LMFDB) 3.16.ah_aq_iq $2$ (not in LMFDB) 3.16.h_aq_aiq $2$ (not in LMFDB) 3.16.j_a_age $2$ (not in LMFDB) 3.16.x_iq_bto $2$ (not in LMFDB) 3.16.al_bs_aey $3$ (not in LMFDB) 3.16.b_i_adc $3$ (not in LMFDB) 3.16.ap_ea_asm $4$ (not in LMFDB) 3.16.ah_bw_aiq $4$ (not in LMFDB) 3.16.ab_ai_abg $4$ (not in LMFDB) 3.16.b_ai_bg $4$ (not in LMFDB) 3.16.h_bw_iq $4$ (not in LMFDB) 3.16.p_ea_sm $4$ (not in LMFDB) 3.16.ad_e_q $5$ (not in LMFDB) 3.16.at_gi_abga $6$ (not in LMFDB) 3.16.ap_eq_awu $6$ (not in LMFDB) 3.16.ah_bg_aei $6$ (not in LMFDB) 3.16.af_ae_cm $6$ (not in LMFDB) 3.16.ad_am_ey $6$ (not in LMFDB) 3.16.ab_i_dc $6$ (not in LMFDB) 3.16.d_am_aey $6$ (not in LMFDB) 3.16.f_ae_acm $6$ (not in LMFDB) 3.16.h_bg_ei $6$ (not in LMFDB) 3.16.l_bs_ey $6$ (not in LMFDB) 3.16.p_eq_wu $6$ (not in LMFDB) 3.16.t_gi_bga $6$ (not in LMFDB) 3.16.ah_q_a $8$ (not in LMFDB) 3.16.h_q_a $8$ (not in LMFDB) 3.16.al_ci_ajg $10$ (not in LMFDB) 3.16.d_e_aq $10$ (not in LMFDB) 3.16.l_ci_jg $10$ (not in LMFDB) 3.16.al_cy_ano $12$ (not in LMFDB) 3.16.ah_a_ei $12$ (not in LMFDB) 3.16.ad_u_ads $12$ (not in LMFDB) 3.16.d_u_ds $12$ (not in LMFDB) 3.16.h_a_aei $12$ (not in LMFDB) 3.16.l_cy_no $12$ (not in LMFDB)