Properties

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

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Invariants

Base field:  $\F_{2}$
Dimension:  $5$
L-polynomial:  $( 1 - 2 x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$
Frobenius angles:  $\pm0.0516399385854$, $\pm0.123548644961$, $\pm0.250000000000$, $\pm0.456881978294$, $\pm0.718306605252$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 1 665 15808 1107225 29590151 1177379840 45108385589 917031425625 32442795501376 1266342321457325

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 3 3 19 27 69 165 211 471 1143

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac $\times$ 2.2.ad_f $\times$ 2.2.ab_ab 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 2 $\times$ 1.4096.ey. 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.ae_h_ac_ap_bi$2$(not in LMFDB)
5.2.ac_b_ae_j_ak$2$(not in LMFDB)
5.2.a_ab_ac_b_c$2$(not in LMFDB)
5.2.a_ab_c_b_ac$2$(not in LMFDB)
5.2.c_b_e_j_k$2$(not in LMFDB)
5.2.e_h_c_ap_abi$2$(not in LMFDB)
5.2.g_r_bg_bx_cs$2$(not in LMFDB)
5.2.ad_c_b_h_aw$3$(not in LMFDB)
5.2.ad_i_ar_bf_abu$3$(not in LMFDB)
5.2.a_ab_ac_b_c$3$(not in LMFDB)
5.2.a_c_ac_h_c$3$(not in LMFDB)
5.2.d_i_n_t_ba$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.2.ae_h_ac_ap_bi$2$(not in LMFDB)
5.2.ac_b_ae_j_ak$2$(not in LMFDB)
5.2.a_ab_ac_b_c$2$(not in LMFDB)
5.2.a_ab_c_b_ac$2$(not in LMFDB)
5.2.c_b_e_j_k$2$(not in LMFDB)
5.2.e_h_c_ap_abi$2$(not in LMFDB)
5.2.g_r_bg_bx_cs$2$(not in LMFDB)
5.2.ad_c_b_h_aw$3$(not in LMFDB)
5.2.ad_i_ar_bf_abu$3$(not in LMFDB)
5.2.a_ab_ac_b_c$3$(not in LMFDB)
5.2.a_c_ac_h_c$3$(not in LMFDB)
5.2.d_i_n_t_ba$3$(not in LMFDB)
5.2.ah_bc_acz_gd_aju$6$(not in LMFDB)
5.2.af_q_abl_cr_aec$6$(not in LMFDB)
5.2.ae_k_ao_p_ao$6$(not in LMFDB)
5.2.ad_i_an_t_aba$6$(not in LMFDB)
5.2.ac_e_ae_j_ak$6$(not in LMFDB)
5.2.ab_ac_h_d_ao$6$(not in LMFDB)
5.2.ab_e_af_j_ao$6$(not in LMFDB)
5.2.ab_e_b_d_k$6$(not in LMFDB)
5.2.a_c_c_h_ac$6$(not in LMFDB)
5.2.b_ac_ah_d_o$6$(not in LMFDB)
5.2.b_e_ab_d_ak$6$(not in LMFDB)
5.2.b_e_f_j_o$6$(not in LMFDB)
5.2.c_e_e_j_k$6$(not in LMFDB)
5.2.d_c_ab_h_w$6$(not in LMFDB)
5.2.d_i_r_bf_bu$6$(not in LMFDB)
5.2.e_k_o_p_o$6$(not in LMFDB)
5.2.f_q_bl_cr_ec$6$(not in LMFDB)
5.2.h_bc_cz_gd_ju$6$(not in LMFDB)
5.2.ae_j_as_bd_abo$8$(not in LMFDB)
5.2.ac_d_a_ah_q$8$(not in LMFDB)
5.2.c_d_a_ah_aq$8$(not in LMFDB)
5.2.e_j_s_bd_bo$8$(not in LMFDB)
5.2.af_k_ah_aj_ba$12$(not in LMFDB)
5.2.ae_m_aw_bl_aby$12$(not in LMFDB)
5.2.ad_e_af_n_aba$12$(not in LMFDB)
5.2.ac_ac_i_d_aw$12$(not in LMFDB)
5.2.ac_a_e_b_ak$12$(not in LMFDB)
5.2.ac_g_ai_t_aw$12$(not in LMFDB)
5.2.ab_ac_b_d_ac$12$(not in LMFDB)
5.2.ab_a_f_b_ac$12$(not in LMFDB)
5.2.a_e_ac_n_ac$12$(not in LMFDB)
5.2.a_e_c_n_c$12$(not in LMFDB)
5.2.b_ac_ab_d_c$12$(not in LMFDB)
5.2.b_a_af_b_c$12$(not in LMFDB)
5.2.c_ac_ai_d_w$12$(not in LMFDB)
5.2.c_a_ae_b_k$12$(not in LMFDB)
5.2.c_g_i_t_w$12$(not in LMFDB)
5.2.d_e_f_n_ba$12$(not in LMFDB)
5.2.e_m_w_bl_by$12$(not in LMFDB)
5.2.f_k_h_aj_aba$12$(not in LMFDB)
5.2.af_s_abt_dl_afk$24$(not in LMFDB)
5.2.ad_e_ad_ad_m$24$(not in LMFDB)
5.2.ad_k_av_bn_aci$24$(not in LMFDB)
5.2.ac_g_ag_l_ai$24$(not in LMFDB)
5.2.ac_i_ak_z_ay$24$(not in LMFDB)
5.2.ab_a_ad_f_ae$24$(not in LMFDB)
5.2.ab_c_af_h_am$24$(not in LMFDB)
5.2.ab_g_aj_r_abc$24$(not in LMFDB)
5.2.a_ac_a_d_a$24$(not in LMFDB)
5.2.a_a_a_b_a$24$(not in LMFDB)
5.2.a_e_a_j_a$24$(not in LMFDB)
5.2.a_g_a_t_a$24$(not in LMFDB)
5.2.b_a_d_f_e$24$(not in LMFDB)
5.2.b_c_f_h_m$24$(not in LMFDB)
5.2.b_g_j_r_bc$24$(not in LMFDB)
5.2.c_g_g_l_i$24$(not in LMFDB)
5.2.c_i_k_z_y$24$(not in LMFDB)
5.2.d_e_d_ad_am$24$(not in LMFDB)
5.2.d_k_v_bn_ci$24$(not in LMFDB)
5.2.f_s_bt_dl_fk$24$(not in LMFDB)