Properties

Label 6.2.aj_bq_afb_lu_avy_bhw
Base Field $\F_{2}$
Dimension $6$
Ordinary No
$p$-rank $3$
Principally polarizable Yes
Contains a Jacobian No

Learn more about

Invariants

Base field:  $\F_{2}$
Dimension:  $6$
L-polynomial:  $( 1 - 2 x + 2 x^{2} )^{3}( 1 - 3 x + 6 x^{2} - 9 x^{3} + 12 x^{4} - 12 x^{5} + 8 x^{6} )$
Frobenius angles:  $\pm0.147012170705$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.341962716420$, $\pm0.600633654388$
Angle rank:  $3$ (numerical)

This isogeny class is not simple.

Newton polygon

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1, 1, 1]$

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3 19125 1127061 88453125 3233980083 64665124875 2947700052888 255414501703125 17508803066335269 1110720565694109375

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 8 21 44 69 59 78 236 498 983

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac 3 $\times$ 3.2.ad_g_aj and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
Endomorphism algebra over $\overline{\F}_{2}$
The base change of $A$ to $\F_{2^{4}}$ is 1.16.i 3 $\times$ 3.16.d_bq_db. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{2^{4}}$.
Remainder of endomorphism lattice by field

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
6.2.af_o_abb_bu_acw_ei$2$(not in LMFDB)
6.2.ad_g_af_g_ag_q$2$(not in LMFDB)
6.2.ab_c_ad_k_ak_q$2$(not in LMFDB)
6.2.b_c_d_k_k_q$2$(not in LMFDB)
6.2.d_g_f_g_g_q$2$(not in LMFDB)
6.2.f_o_bb_bu_cw_ei$2$(not in LMFDB)
6.2.j_bq_fb_lu_vy_bhw$2$(not in LMFDB)
6.2.ad_g_af_a_m_au$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
6.2.af_o_abb_bu_acw_ei$2$(not in LMFDB)
6.2.ad_g_af_g_ag_q$2$(not in LMFDB)
6.2.ab_c_ad_k_ak_q$2$(not in LMFDB)
6.2.b_c_d_k_k_q$2$(not in LMFDB)
6.2.d_g_f_g_g_q$2$(not in LMFDB)
6.2.f_o_bb_bu_cw_ei$2$(not in LMFDB)
6.2.j_bq_fb_lu_vy_bhw$2$(not in LMFDB)
6.2.ad_g_af_a_m_au$3$(not in LMFDB)
6.2.ah_ba_acr_fs_aki_pw$6$(not in LMFDB)
6.2.ad_g_an_y_abk_ca$6$(not in LMFDB)
6.2.ab_c_ad_e_ae_e$6$(not in LMFDB)
6.2.b_c_d_e_e_e$6$(not in LMFDB)
6.2.d_g_f_a_am_au$6$(not in LMFDB)
6.2.d_g_n_y_bk_ca$6$(not in LMFDB)
6.2.h_ba_cr_fs_ki_pw$6$(not in LMFDB)
6.2.ah_bc_adb_gu_amk_tc$8$(not in LMFDB)
6.2.af_k_ah_ak_bi_ace$8$(not in LMFDB)
6.2.af_s_abv_dy_aha_ku$8$(not in LMFDB)
6.2.ad_e_ad_ae_s_abg$8$(not in LMFDB)
6.2.ad_i_ap_bc_abq_cm$8$(not in LMFDB)
6.2.ad_m_abb_ci_ady_ge$8$(not in LMFDB)
6.2.ab_ac_b_c_c_ai$8$(not in LMFDB)
6.2.ab_e_ab_i_c_q$8$(not in LMFDB)
6.2.ab_g_ah_s_aw_bo$8$(not in LMFDB)
6.2.b_ac_ab_c_ac_ai$8$(not in LMFDB)
6.2.b_e_b_i_ac_q$8$(not in LMFDB)
6.2.b_g_h_s_w_bo$8$(not in LMFDB)
6.2.d_e_d_ae_as_abg$8$(not in LMFDB)
6.2.d_i_p_bc_bq_cm$8$(not in LMFDB)
6.2.d_m_bb_ci_dy_ge$8$(not in LMFDB)
6.2.f_k_h_ak_abi_ace$8$(not in LMFDB)
6.2.f_s_bv_dy_ha_ku$8$(not in LMFDB)
6.2.h_bc_db_gu_mk_tc$8$(not in LMFDB)
6.2.af_m_ar_s_au_bc$24$(not in LMFDB)
6.2.af_q_abp_di_afw_iy$24$(not in LMFDB)
6.2.af_q_abl_cw_aey_ho$24$(not in LMFDB)
6.2.ad_g_aj_m_am_q$24$(not in LMFDB)
6.2.ad_k_av_bs_acu_ei$24$(not in LMFDB)
6.2.ab_a_ab_g_ae_e$24$(not in LMFDB)
6.2.ab_e_af_o_aq_bc$24$(not in LMFDB)
6.2.ab_e_ab_c_i_ai$24$(not in LMFDB)
6.2.b_a_b_g_e_e$24$(not in LMFDB)
6.2.b_e_b_c_ai_ai$24$(not in LMFDB)
6.2.b_e_f_o_q_bc$24$(not in LMFDB)
6.2.d_g_j_m_m_q$24$(not in LMFDB)
6.2.d_k_v_bs_cu_ei$24$(not in LMFDB)
6.2.f_m_r_s_u_bc$24$(not in LMFDB)
6.2.f_q_bl_cw_ey_ho$24$(not in LMFDB)
6.2.f_q_bp_di_fw_iy$24$(not in LMFDB)