Properties

Label 5.2.ai_bi_adt_hw_amq
Base Field $\F_{2}$
Dimension $5$
Ordinary No
$p$-rank $3$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{2}$
Dimension:  $5$
L-polynomial:  $( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$
Frobenius angles:  $\pm0.123548644961$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.384973271919$, $\pm0.456881978294$
Angle rank:  $2$ (numerical)

This isogeny class is not simple.

Newton polygon

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

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 3800 179816 1710000 35539702 1366601600 39982829098 1019710620000 31323168057272 1132739151995000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 9 22 25 35 78 149 241 454 1029

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac 2 $\times$ 1.2.ab $\times$ 2.2.ad_f 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 $\F_{2^{12}}$ is 1.4096.h 2 $\times$ 1.4096.bv $\times$ 1.4096.ey 2 . The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{2^{12}}$.
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.ag_u_abv_dk_afg$2$(not in LMFDB)
5.2.ae_k_ar_y_abg$2$(not in LMFDB)
5.2.ac_e_ah_m_aq$2$(not in LMFDB)
5.2.ac_e_ab_a_i$2$(not in LMFDB)
5.2.a_c_ab_e_ai$2$(not in LMFDB)
5.2.a_c_b_e_i$2$(not in LMFDB)
5.2.c_e_b_a_ai$2$(not in LMFDB)
5.2.c_e_h_m_q$2$(not in LMFDB)
5.2.e_k_r_y_bg$2$(not in LMFDB)
5.2.g_u_bv_dk_fg$2$(not in LMFDB)
5.2.i_bi_dt_hw_mq$2$(not in LMFDB)
5.2.af_n_at_s_aq$3$(not in LMFDB)
5.2.ac_e_ab_ag_o$3$(not in LMFDB)
5.2.ac_e_ab_a_i$3$(not in LMFDB)
5.2.b_b_f_g_c$3$(not in LMFDB)
5.2.e_k_x_bq_ck$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.2.ag_u_abv_dk_afg$2$(not in LMFDB)
5.2.ae_k_ar_y_abg$2$(not in LMFDB)
5.2.ac_e_ah_m_aq$2$(not in LMFDB)
5.2.ac_e_ab_a_i$2$(not in LMFDB)
5.2.a_c_ab_e_ai$2$(not in LMFDB)
5.2.a_c_b_e_i$2$(not in LMFDB)
5.2.c_e_b_a_ai$2$(not in LMFDB)
5.2.c_e_h_m_q$2$(not in LMFDB)
5.2.e_k_r_y_bg$2$(not in LMFDB)
5.2.g_u_bv_dk_fg$2$(not in LMFDB)
5.2.i_bi_dt_hw_mq$2$(not in LMFDB)
5.2.af_n_at_s_aq$3$(not in LMFDB)
5.2.ac_e_ab_ag_o$3$(not in LMFDB)
5.2.ac_e_ab_a_i$3$(not in LMFDB)
5.2.b_b_f_g_c$3$(not in LMFDB)
5.2.e_k_x_bq_ck$3$(not in LMFDB)
5.2.ag_u_abx_dq_afq$6$(not in LMFDB)
5.2.ae_k_ax_bq_ack$6$(not in LMFDB)
5.2.ad_f_ah_k_ao$6$(not in LMFDB)
5.2.ad_f_af_k_aq$6$(not in LMFDB)
5.2.ab_b_af_g_ac$6$(not in LMFDB)
5.2.ab_b_b_g_ai$6$(not in LMFDB)
5.2.a_c_ab_ac_ac$6$(not in LMFDB)
5.2.a_c_b_ac_c$6$(not in LMFDB)
5.2.b_b_ab_g_i$6$(not in LMFDB)
5.2.c_e_b_ag_ao$6$(not in LMFDB)
5.2.d_f_f_k_q$6$(not in LMFDB)
5.2.d_f_h_k_o$6$(not in LMFDB)
5.2.f_n_t_s_q$6$(not in LMFDB)
5.2.g_u_bx_dq_fq$6$(not in LMFDB)
5.2.ag_w_acf_ek_agy$8$(not in LMFDB)
5.2.ae_g_ab_aq_bk$8$(not in LMFDB)
5.2.ae_m_abb_by_acy$8$(not in LMFDB)
5.2.ae_o_abh_cm_adw$8$(not in LMFDB)
5.2.ac_a_b_ae_m$8$(not in LMFDB)
5.2.ac_g_aj_o_au$8$(not in LMFDB)
5.2.ac_i_ap_bc_abs$8$(not in LMFDB)
5.2.a_e_ad_g_am$8$(not in LMFDB)
5.2.a_e_d_g_m$8$(not in LMFDB)
5.2.c_a_ab_ae_am$8$(not in LMFDB)
5.2.c_g_j_o_u$8$(not in LMFDB)
5.2.c_i_p_bc_bs$8$(not in LMFDB)
5.2.e_g_b_aq_abk$8$(not in LMFDB)
5.2.e_m_bb_by_cy$8$(not in LMFDB)
5.2.e_o_bh_cm_dw$8$(not in LMFDB)
5.2.g_w_cf_ek_gy$8$(not in LMFDB)
5.2.af_p_abd_bu_acm$12$(not in LMFDB)
5.2.ad_h_an_w_abi$12$(not in LMFDB)
5.2.ad_h_al_w_abg$12$(not in LMFDB)
5.2.ab_d_ah_k_ao$12$(not in LMFDB)
5.2.ab_d_ab_k_ai$12$(not in LMFDB)
5.2.a_c_b_ac_c$12$(not in LMFDB)
5.2.b_d_b_k_i$12$(not in LMFDB)
5.2.b_d_h_k_o$12$(not in LMFDB)
5.2.d_h_l_w_bg$12$(not in LMFDB)
5.2.d_h_n_w_bi$12$(not in LMFDB)
5.2.f_p_bd_bu_cm$12$(not in LMFDB)
5.2.ae_i_aj_e_c$24$(not in LMFDB)
5.2.ae_m_az_bs_aco$24$(not in LMFDB)
5.2.ad_h_aj_m_am$24$(not in LMFDB)
5.2.ad_j_ap_bc_abk$24$(not in LMFDB)
5.2.ac_c_ad_e_ac$24$(not in LMFDB)
5.2.ac_g_al_u_abe$24$(not in LMFDB)
5.2.ab_ad_f_c_am$24$(not in LMFDB)
5.2.ab_ab_d_ac_ae$24$(not in LMFDB)
5.2.ab_ab_d_e_ak$24$(not in LMFDB)
5.2.ab_b_b_e_ag$24$(not in LMFDB)
5.2.ab_d_ad_i_ae$24$(not in LMFDB)
5.2.ab_d_ab_i_ag$24$(not in LMFDB)
5.2.ab_f_af_q_am$24$(not in LMFDB)
5.2.ab_f_ad_k_ae$24$(not in LMFDB)
5.2.ab_f_ad_q_ak$24$(not in LMFDB)
5.2.ab_h_af_w_am$24$(not in LMFDB)
5.2.b_ad_af_c_m$24$(not in LMFDB)
5.2.b_ab_ad_ac_e$24$(not in LMFDB)
5.2.b_ab_ad_e_k$24$(not in LMFDB)
5.2.b_b_ab_e_g$24$(not in LMFDB)
5.2.b_d_b_i_g$24$(not in LMFDB)
5.2.b_d_d_i_e$24$(not in LMFDB)
5.2.b_f_d_k_e$24$(not in LMFDB)
5.2.b_f_d_q_k$24$(not in LMFDB)
5.2.b_f_f_q_m$24$(not in LMFDB)
5.2.b_h_f_w_m$24$(not in LMFDB)
5.2.c_c_d_e_c$24$(not in LMFDB)
5.2.c_g_l_u_be$24$(not in LMFDB)
5.2.d_h_j_m_m$24$(not in LMFDB)
5.2.d_j_p_bc_bk$24$(not in LMFDB)
5.2.e_i_j_e_ac$24$(not in LMFDB)
5.2.e_m_z_bs_co$24$(not in LMFDB)