Properties

Label 5.2.ag_r_abd_bj_abq
Base Field $\F_{2}$
Dimension $5$
Ordinary No
$p$-rank $4$
Principally polarizable Yes
Contains a Jacobian No

Learn more about

Invariants

Base field:  $\F_{2}$
Dimension:  $5$
L-polynomial:  $( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$
Frobenius angles:  $\pm0.0992589862044$, $\pm0.186455299510$, $\pm0.250000000000$, $\pm0.384973271919$, $\pm0.757883870938$
Angle rank:  $1$ (numerical)

This isogeny class is not simple.

Newton polygon

$p$-rank:  $4$
Slopes:  $[0, 0, 0, 0, 1/2, 1/2, 1, 1, 1, 1]$

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
$A(\F_{q^r})$ 2 1160 54782 3259600 31444622 1366263080 45944319248 1065087338400 37325861913158 1054240697331800

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 3 12 35 32 78 165 251 543 958

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac $\times$ 1.2.ab $\times$ 3.2.ad_c_b 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 $\F_{2^{28}}$ is 1.268435456.blhf 4 $\times$ 1.268435456.bwmi. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{2^{28}}$.
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
5.2.ae_h_aj_r_abe$2$(not in LMFDB)
5.2.ac_b_ab_h_ao$2$(not in LMFDB)
5.2.a_ab_af_f_g$2$(not in LMFDB)
5.2.a_ab_f_f_ag$2$(not in LMFDB)
5.2.c_b_b_h_o$2$(not in LMFDB)
5.2.e_h_j_r_be$2$(not in LMFDB)
5.2.g_r_bd_bj_bq$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.2.ae_h_aj_r_abe$2$(not in LMFDB)
5.2.ac_b_ab_h_ao$2$(not in LMFDB)
5.2.a_ab_af_f_g$2$(not in LMFDB)
5.2.a_ab_f_f_ag$2$(not in LMFDB)
5.2.c_b_b_h_o$2$(not in LMFDB)
5.2.e_h_j_r_be$2$(not in LMFDB)
5.2.g_r_bd_bj_bq$2$(not in LMFDB)
5.2.ag_y_acm_fd_aic$7$(not in LMFDB)
5.2.b_d_g_h_o$7$(not in LMFDB)
5.2.ae_j_ap_v_abc$8$(not in LMFDB)
5.2.ac_d_ah_l_am$8$(not in LMFDB)
5.2.c_d_h_l_m$8$(not in LMFDB)
5.2.e_j_p_v_bc$8$(not in LMFDB)
5.2.ah_bb_acu_fp_aiw$14$(not in LMFDB)
5.2.af_p_abi_cl_adu$14$(not in LMFDB)
5.2.ae_o_abe_ch_adi$14$(not in LMFDB)
5.2.ad_h_am_r_aba$14$(not in LMFDB)
5.2.ac_i_am_bd_abi$14$(not in LMFDB)
5.2.ac_i_ai_v_ao$14$(not in LMFDB)
5.2.ab_d_ag_h_ao$14$(not in LMFDB)
5.2.a_g_ac_t_ag$14$(not in LMFDB)
5.2.a_g_c_t_g$14$(not in LMFDB)
5.2.c_i_i_v_o$14$(not in LMFDB)
5.2.c_i_m_bd_bi$14$(not in LMFDB)
5.2.d_h_m_r_ba$14$(not in LMFDB)
5.2.e_o_be_ch_di$14$(not in LMFDB)
5.2.f_p_bi_cl_du$14$(not in LMFDB)
5.2.g_y_cm_fd_ic$14$(not in LMFDB)
5.2.h_bb_cu_fp_iw$14$(not in LMFDB)
5.2.ad_g_ab_al_be$21$(not in LMFDB)
5.2.a_ad_i_h_as$21$(not in LMFDB)
5.2.ae_i_ag_ah_w$28$(not in LMFDB)
5.2.ac_ae_m_f_abi$28$(not in LMFDB)
5.2.ac_c_a_ab_c$28$(not in LMFDB)
5.2.a_a_ac_b_g$28$(not in LMFDB)
5.2.a_a_c_b_ag$28$(not in LMFDB)
5.2.c_ae_am_f_bi$28$(not in LMFDB)
5.2.c_c_a_ab_ac$28$(not in LMFDB)
5.2.e_i_g_ah_aw$28$(not in LMFDB)
5.2.ab_ab_b_d_ak$35$(not in LMFDB)
5.2.af_o_abb_bp_acg$42$(not in LMFDB)
5.2.ae_f_ae_p_abi$42$(not in LMFDB)
5.2.ad_g_al_t_abe$42$(not in LMFDB)
5.2.ac_ab_g_ab_ak$42$(not in LMFDB)
5.2.ab_c_ah_j_ak$42$(not in LMFDB)
5.2.ab_c_ad_f_ao$42$(not in LMFDB)
5.2.ab_c_d_ab_k$42$(not in LMFDB)
5.2.a_ad_ai_h_s$42$(not in LMFDB)
5.2.b_c_ad_ab_ak$42$(not in LMFDB)
5.2.b_c_d_f_o$42$(not in LMFDB)
5.2.b_c_h_j_k$42$(not in LMFDB)
5.2.c_ab_ag_ab_k$42$(not in LMFDB)
5.2.d_g_b_al_abe$42$(not in LMFDB)
5.2.d_g_l_t_be$42$(not in LMFDB)
5.2.e_f_e_p_bi$42$(not in LMFDB)
5.2.f_o_bb_bp_cg$42$(not in LMFDB)
5.2.af_r_abq_dd_aey$56$(not in LMFDB)
5.2.ae_q_abk_cz_aei$56$(not in LMFDB)
5.2.ad_j_au_bj_ace$56$(not in LMFDB)
5.2.ac_c_a_b_ac$56$(not in LMFDB)
5.2.ac_e_ac_ad_i$56$(not in LMFDB)
5.2.ac_k_ao_bn_abo$56$(not in LMFDB)
5.2.a_ae_a_f_a$56$(not in LMFDB)
5.2.a_c_a_ab_a$56$(not in LMFDB)
5.2.a_c_a_b_a$56$(not in LMFDB)
5.2.a_i_a_bd_a$56$(not in LMFDB)
5.2.c_c_a_b_c$56$(not in LMFDB)
5.2.c_e_c_ad_ai$56$(not in LMFDB)
5.2.c_k_o_bn_bo$56$(not in LMFDB)
5.2.d_j_u_bj_ce$56$(not in LMFDB)
5.2.e_q_bk_cz_ei$56$(not in LMFDB)
5.2.f_r_bq_dd_ey$56$(not in LMFDB)
5.2.ad_d_d_aj_o$70$(not in LMFDB)
5.2.b_ab_ab_d_k$70$(not in LMFDB)
5.2.d_d_ad_aj_ao$70$(not in LMFDB)
5.2.ad_a_h_b_as$84$(not in LMFDB)
5.2.ac_f_ag_l_ak$84$(not in LMFDB)
5.2.ab_ae_j_f_aba$84$(not in LMFDB)
5.2.b_ae_aj_f_ba$84$(not in LMFDB)
5.2.c_f_g_l_k$84$(not in LMFDB)
5.2.d_a_ah_b_s$84$(not in LMFDB)
5.2.ad_i_ap_x_abk$168$(not in LMFDB)
5.2.ac_b_ag_l_ai$168$(not in LMFDB)
5.2.ab_ac_ab_d_e$168$(not in LMFDB)
5.2.ab_e_ah_j_au$168$(not in LMFDB)
5.2.ab_e_d_ab_u$168$(not in LMFDB)
5.2.a_ab_a_ab_a$168$(not in LMFDB)
5.2.a_f_a_l_a$168$(not in LMFDB)
5.2.b_ac_b_d_ae$168$(not in LMFDB)
5.2.b_e_ad_ab_au$168$(not in LMFDB)
5.2.b_e_h_j_u$168$(not in LMFDB)
5.2.c_b_g_l_i$168$(not in LMFDB)
5.2.d_i_p_x_bk$168$(not in LMFDB)
5.2.ab_b_b_ad_m$280$(not in LMFDB)
5.2.b_b_ab_ad_am$280$(not in LMFDB)