# Properties

 Label 6.2.aj_bq_aff_ms_ayp_bmn Base Field $\F_{2}$ Dimension $6$ Ordinary Yes $p$-rank $6$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{2}$ Dimension: $6$ L-polynomial: $( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )^{3}$ Frobenius angles: $\pm0.123548644961$, $\pm0.123548644961$, $\pm0.123548644961$, $\pm0.456881978294$, $\pm0.456881978294$, $\pm0.456881978294$ Angle rank: $1$ (numerical)

This isogeny class is not simple.

## Newton polygon

This isogeny class is ordinary.

 $p$-rank: $6$ Slopes: $[0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1]$

## 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 $A(\F_{q^r})$ 1 6859 438976 5000211 887503681 192699928576 10722223798651 342104081183019 17854072924596544 1381721358424021399

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -6 8 9 -4 24 131 246 308 513 1208

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
 The isogeny class factors as 2.2.ad_f 3 and its endomorphism algebra is $\mathrm{M}_{3}($$$\Q(\sqrt{-3}, \sqrt{5})$$$)$
Endomorphism algebra over $\overline{\F}_{2}$
 The base change of $A$ to $\F_{2^{6}}$ is 1.64.l 6 and its endomorphism algebra is $\mathrm{M}_{6}($$$\Q(\sqrt{-15})$$$)$
All geometric endomorphisms are defined over $\F_{2^{6}}$.
Remainder of endomorphism lattice by field
• Endomorphism algebra over $\F_{2^{2}}$  The base change of $A$ to $\F_{2^{2}}$ is 2.4.b_ad 3 and its endomorphism algebra is $\mathrm{M}_{3}($$$\Q(\sqrt{-3}, \sqrt{5})$$$)$
• Endomorphism algebra over $\F_{2^{3}}$  The base change of $A$ to $\F_{2^{3}}$ is 2.8.a_l 3 and its endomorphism algebra is $\mathrm{M}_{3}($$$\Q(\sqrt{-3}, \sqrt{5})$$$)$

## 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 6.2.ad_g_aj_g_d_ah $2$ (not in LMFDB) 6.2.d_g_j_g_ad_ah $2$ (not in LMFDB) 6.2.j_bq_ff_ms_yp_bmn $2$ (not in LMFDB) 6.2.ag_s_abk_cc_aco_df $3$ (not in LMFDB) 6.2.ad_d_a_d_ap_bd $3$ (not in LMFDB) 6.2.ad_g_aj_g_d_ah $3$ (not in LMFDB) 6.2.a_ad_a_p_a_az $3$ (not in LMFDB) 6.2.a_a_a_a_a_l $3$ (not in LMFDB) 6.2.d_d_a_d_p_bd $3$ (not in LMFDB) 6.2.d_g_j_g_ad_ah $3$ (not in LMFDB) 6.2.g_s_bk_cc_co_df $3$ (not in LMFDB) 6.2.j_bq_ff_ms_yp_bmn $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 6.2.ad_g_aj_g_d_ah $2$ (not in LMFDB) 6.2.d_g_j_g_ad_ah $2$ (not in LMFDB) 6.2.j_bq_ff_ms_yp_bmn $2$ (not in LMFDB) 6.2.ag_s_abk_cc_aco_df $3$ (not in LMFDB) 6.2.ad_d_a_d_ap_bd $3$ (not in LMFDB) 6.2.ad_g_aj_g_d_ah $3$ (not in LMFDB) 6.2.a_ad_a_p_a_az $3$ (not in LMFDB) 6.2.a_a_a_a_a_l $3$ (not in LMFDB) 6.2.d_d_a_d_p_bd $3$ (not in LMFDB) 6.2.d_g_j_g_ad_ah $3$ (not in LMFDB) 6.2.g_s_bk_cc_co_df $3$ (not in LMFDB) 6.2.j_bq_ff_ms_yp_bmn $3$ (not in LMFDB) 6.2.ad_e_ad_ae_p_ax $4$ (not in LMFDB) 6.2.d_e_d_ae_ap_ax $4$ (not in LMFDB) 6.2.ae_m_az_bt_acr_dx $5$ (not in LMFDB) 6.2.b_ad_af_a_g_l $5$ (not in LMFDB) 6.2.d_g_j_g_ad_ah $6$ (not in LMFDB) 6.2.a_a_aj_a_a_bj $9$ (not in LMFDB) 6.2.a_a_j_a_a_bj $9$ (not in LMFDB) 6.2.ah_v_abf_g_cu_agb $10$ (not in LMFDB) 6.2.ac_g_al_v_abh_cb $10$ (not in LMFDB) 6.2.ab_ad_f_a_ag_l $10$ (not in LMFDB) 6.2.c_g_l_v_bh_cb $10$ (not in LMFDB) 6.2.e_m_z_bt_cr_dx $10$ (not in LMFDB) 6.2.h_v_bf_g_acu_agb $10$ (not in LMFDB) 6.2.ag_u_abw_do_afu_in $12$ (not in LMFDB) 6.2.ad_f_ag_l_av_bj $12$ (not in LMFDB) 6.2.ad_h_am_x_abn_cj $12$ (not in LMFDB) 6.2.a_ac_a_c_a_af $12$ (not in LMFDB) 6.2.a_ab_a_l_a_ah $12$ (not in LMFDB) 6.2.a_a_a_a_a_al $12$ (not in LMFDB) 6.2.a_b_a_l_a_h $12$ (not in LMFDB) 6.2.a_c_a_c_a_f $12$ (not in LMFDB) 6.2.a_d_a_p_a_z $12$ (not in LMFDB) 6.2.d_f_g_l_v_bj $12$ (not in LMFDB) 6.2.d_h_m_x_bn_cj $12$ (not in LMFDB) 6.2.g_u_bw_do_fu_in $12$ (not in LMFDB) 6.2.ai_bh_adr_if_apa_xb $15$ (not in LMFDB) 6.2.ah_v_abf_g_cu_agb $15$ (not in LMFDB) 6.2.af_m_au_be_abt_cn $15$ (not in LMFDB) 6.2.ae_d_l_av_aj_cb $15$ (not in LMFDB) 6.2.ac_d_af_d_a_ab $15$ (not in LMFDB) 6.2.ac_g_al_v_abh_cb $15$ (not in LMFDB) 6.2.ab_ad_f_a_ag_l $15$ (not in LMFDB) 6.2.ab_d_ab_j_ag_x $15$ (not in LMFDB) 6.2.b_d_b_j_g_x $15$ (not in LMFDB) 6.2.c_d_f_d_a_ab $15$ (not in LMFDB) 6.2.c_g_l_v_bh_cb $15$ (not in LMFDB) 6.2.e_d_al_av_j_cb $15$ (not in LMFDB) 6.2.e_m_z_bt_cr_dx $15$ (not in LMFDB) 6.2.f_m_u_be_bt_cn $15$ (not in LMFDB) 6.2.h_v_bf_g_acu_agb $15$ (not in LMFDB) 6.2.i_bh_dr_if_pa_xb $15$ (not in LMFDB) 6.2.ad_f_ag_ad_v_abj $24$ (not in LMFDB) 6.2.a_ab_a_ad_a_h $24$ (not in LMFDB) 6.2.a_b_a_ad_a_ah $24$ (not in LMFDB) 6.2.d_f_g_ad_av_abj $24$ (not in LMFDB) 6.2.af_o_abe_ce_adr_fn $60$ (not in LMFDB) 6.2.ae_f_d_an_f_l $60$ (not in LMFDB) 6.2.ab_f_ad_r_ak_bp $60$ (not in LMFDB) 6.2.b_f_d_r_k_bp $60$ (not in LMFDB) 6.2.e_f_ad_an_af_l $60$ (not in LMFDB) 6.2.f_o_be_ce_dr_fn $60$ (not in LMFDB)