Properties

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

Learn more about

Invariants

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

This isogeny class is not simple.

Newton polygon

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

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 4275 115596 961875 53309553 1976691600 36322429251 796648921875 31020820875252 1274331545994375

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 10 17 18 46 103 136 178 449 1150

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac 2 $\times$ 1.2.a $\times$ 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 $\F_{2^{24}}$ is 1.16777216.amdc 3 $\times$ 1.16777216.mbf 2 . The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{2^{24}}$.
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.ad_h_am_s_ay$2$(not in LMFDB)
5.2.ab_d_a_c_i$2$(not in LMFDB)
5.2.b_d_a_c_ai$2$(not in LMFDB)
5.2.d_h_m_s_y$2$(not in LMFDB)
5.2.h_bb_cu_fq_iy$2$(not in LMFDB)
5.2.ae_j_am_o_aq$3$(not in LMFDB)
5.2.ab_d_a_ae_i$3$(not in LMFDB)
5.2.ab_d_a_c_i$3$(not in LMFDB)
5.2.c_d_g_i_i$3$(not in LMFDB)
5.2.f_p_bk_cq_ea$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.2.ad_h_am_s_ay$2$(not in LMFDB)
5.2.ab_d_a_c_i$2$(not in LMFDB)
5.2.b_d_a_c_ai$2$(not in LMFDB)
5.2.d_h_m_s_y$2$(not in LMFDB)
5.2.h_bb_cu_fq_iy$2$(not in LMFDB)
5.2.ae_j_am_o_aq$3$(not in LMFDB)
5.2.ab_d_a_ae_i$3$(not in LMFDB)
5.2.ab_d_a_c_i$3$(not in LMFDB)
5.2.c_d_g_i_i$3$(not in LMFDB)
5.2.f_p_bk_cq_ea$3$(not in LMFDB)
5.2.af_p_abk_cq_aea$6$(not in LMFDB)
5.2.ac_d_ag_i_ai$6$(not in LMFDB)
5.2.a_b_a_g_a$6$(not in LMFDB)
5.2.b_d_a_ae_ai$6$(not in LMFDB)
5.2.e_j_m_o_q$6$(not in LMFDB)
5.2.aj_bp_aes_kc_aqi$8$(not in LMFDB)
5.2.af_j_ac_aw_bw$8$(not in LMFDB)
5.2.af_n_aw_be_abo$8$(not in LMFDB)
5.2.af_r_abq_de_aey$8$(not in LMFDB)
5.2.ad_d_a_ak_y$8$(not in LMFDB)
5.2.ad_f_ac_ac_i$8$(not in LMFDB)
5.2.ad_l_ay_bu_acu$8$(not in LMFDB)
5.2.ab_ad_c_c_a$8$(not in LMFDB)
5.2.ab_b_ac_g_ai$8$(not in LMFDB)
5.2.ab_f_ag_k_aq$8$(not in LMFDB)
5.2.b_ad_ac_c_a$8$(not in LMFDB)
5.2.b_b_c_g_i$8$(not in LMFDB)
5.2.b_f_g_k_q$8$(not in LMFDB)
5.2.d_d_a_ak_ay$8$(not in LMFDB)
5.2.d_f_c_ac_ai$8$(not in LMFDB)
5.2.d_l_y_bu_cu$8$(not in LMFDB)
5.2.f_j_c_aw_abw$8$(not in LMFDB)
5.2.f_n_w_be_bo$8$(not in LMFDB)
5.2.f_r_bq_de_ey$8$(not in LMFDB)
5.2.j_bp_es_kc_qi$8$(not in LMFDB)
5.2.ae_l_au_bi_abw$12$(not in LMFDB)
5.2.ac_f_ak_q_ay$12$(not in LMFDB)
5.2.a_d_a_k_a$12$(not in LMFDB)
5.2.c_f_k_q_y$12$(not in LMFDB)
5.2.e_l_u_bi_bw$12$(not in LMFDB)
5.2.ah_z_ack_eq_ahg$24$(not in LMFDB)
5.2.ag_r_aba_w_aq$24$(not in LMFDB)
5.2.ag_t_abm_cg_adc$24$(not in LMFDB)
5.2.af_l_am_e_e$24$(not in LMFDB)
5.2.af_p_abg_ce_adg$24$(not in LMFDB)
5.2.ae_h_ai_m_au$24$(not in LMFDB)
5.2.ae_j_aq_bc_abs$24$(not in LMFDB)
5.2.ad_f_ak_q_au$24$(not in LMFDB)
5.2.ad_f_ag_e_a$24$(not in LMFDB)
5.2.ad_f_ac_ai_u$24$(not in LMFDB)
5.2.ad_j_as_bg_abw$24$(not in LMFDB)
5.2.ac_ad_k_c_ay$24$(not in LMFDB)
5.2.ac_ab_g_ac_ai$24$(not in LMFDB)
5.2.ac_ab_g_e_au$24$(not in LMFDB)
5.2.ac_b_c_e_am$24$(not in LMFDB)
5.2.ac_b_c_g_aq$24$(not in LMFDB)
5.2.ac_d_ac_i_am$24$(not in LMFDB)
5.2.ac_d_ac_k_aq$24$(not in LMFDB)
5.2.ac_f_ag_k_ai$24$(not in LMFDB)
5.2.ac_f_ag_q_au$24$(not in LMFDB)
5.2.ac_h_ak_w_ay$24$(not in LMFDB)
5.2.ab_ab_a_e_ae$24$(not in LMFDB)
5.2.ab_b_ac_a_e$24$(not in LMFDB)
5.2.ab_d_ae_i_am$24$(not in LMFDB)
5.2.a_ad_a_c_a$24$(not in LMFDB)
5.2.a_ab_ae_e_e$24$(not in LMFDB)
5.2.a_ab_a_ac_a$24$(not in LMFDB)
5.2.a_ab_a_e_a$24$(not in LMFDB)
5.2.a_ab_e_e_ae$24$(not in LMFDB)
5.2.a_b_ae_e_ae$24$(not in LMFDB)
5.2.a_b_a_e_a$24$(not in LMFDB)
5.2.a_b_e_e_e$24$(not in LMFDB)
5.2.a_d_a_i_a$24$(not in LMFDB)
5.2.a_f_a_k_a$24$(not in LMFDB)
5.2.a_f_a_q_a$24$(not in LMFDB)
5.2.a_h_a_w_a$24$(not in LMFDB)
5.2.b_ab_a_e_e$24$(not in LMFDB)
5.2.b_b_c_a_ae$24$(not in LMFDB)
5.2.b_d_e_i_m$24$(not in LMFDB)
5.2.c_ad_ak_c_y$24$(not in LMFDB)
5.2.c_ab_ag_ac_i$24$(not in LMFDB)
5.2.c_ab_ag_e_u$24$(not in LMFDB)
5.2.c_b_ac_e_m$24$(not in LMFDB)
5.2.c_b_ac_g_q$24$(not in LMFDB)
5.2.c_d_c_i_m$24$(not in LMFDB)
5.2.c_d_c_k_q$24$(not in LMFDB)
5.2.c_f_g_k_i$24$(not in LMFDB)
5.2.c_f_g_q_u$24$(not in LMFDB)
5.2.c_h_k_w_y$24$(not in LMFDB)
5.2.d_f_c_ai_au$24$(not in LMFDB)
5.2.d_f_g_e_a$24$(not in LMFDB)
5.2.d_f_k_q_u$24$(not in LMFDB)
5.2.d_j_s_bg_bw$24$(not in LMFDB)
5.2.e_h_i_m_u$24$(not in LMFDB)
5.2.e_j_q_bc_bs$24$(not in LMFDB)
5.2.f_l_m_e_ae$24$(not in LMFDB)
5.2.f_p_bg_ce_dg$24$(not in LMFDB)
5.2.g_r_ba_w_q$24$(not in LMFDB)
5.2.g_t_bm_cg_dc$24$(not in LMFDB)
5.2.h_z_ck_eq_hg$24$(not in LMFDB)