Properties

Label 5.2.ah_bb_acs_fi_aii
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:  $( 1 - 2 x + 2 x^{2} )^{3}( 1 - x + 3 x^{2} - 2 x^{3} + 4 x^{4} )$
Frobenius angles:  $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.306143893905$, $\pm0.570118980449$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 5 6875 175760 4296875 94766375 966680000 16672674835 754913671875 33661378209680 1156445919921875

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 10 23 42 66 55 38 162 491 1050

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac 3 $\times$ 2.2.ab_d 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 $\times$ 2.16.b_b. 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
5.2.af_p_abe_by_acu$2$(not in LMFDB)
5.2.ad_h_ak_s_ay$2$(not in LMFDB)
5.2.ab_d_ac_k_ai$2$(not in LMFDB)
5.2.b_d_c_k_i$2$(not in LMFDB)
5.2.d_h_k_s_y$2$(not in LMFDB)
5.2.f_p_be_by_cu$2$(not in LMFDB)
5.2.h_bb_cs_fi_ii$2$(not in LMFDB)
5.2.ab_d_c_a_m$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.2.af_p_abe_by_acu$2$(not in LMFDB)
5.2.ad_h_ak_s_ay$2$(not in LMFDB)
5.2.ab_d_ac_k_ai$2$(not in LMFDB)
5.2.b_d_c_k_i$2$(not in LMFDB)
5.2.d_h_k_s_y$2$(not in LMFDB)
5.2.f_p_be_by_cu$2$(not in LMFDB)
5.2.h_bb_cs_fi_ii$2$(not in LMFDB)
5.2.ab_d_c_a_m$3$(not in LMFDB)
5.2.af_p_abi_cm_adw$6$(not in LMFDB)
5.2.ad_h_ao_y_abk$6$(not in LMFDB)
5.2.ab_d_ag_i_am$6$(not in LMFDB)
5.2.b_d_ac_a_am$6$(not in LMFDB)
5.2.b_d_g_i_m$6$(not in LMFDB)
5.2.d_h_o_y_bk$6$(not in LMFDB)
5.2.f_p_bi_cm_dw$6$(not in LMFDB)
5.2.af_r_abo_da_aeq$8$(not in LMFDB)
5.2.ad_d_c_ak_q$8$(not in LMFDB)
5.2.ad_j_aq_be_abo$8$(not in LMFDB)
5.2.ad_l_aw_bu_acm$8$(not in LMFDB)
5.2.ab_ab_c_ac_a$8$(not in LMFDB)
5.2.ab_b_a_ag_i$8$(not in LMFDB)
5.2.ab_f_ae_o_ai$8$(not in LMFDB)
5.2.ab_h_ag_w_aq$8$(not in LMFDB)
5.2.ab_j_ai_bi_ay$8$(not in LMFDB)
5.2.b_ab_ac_ac_a$8$(not in LMFDB)
5.2.b_b_a_ag_ai$8$(not in LMFDB)
5.2.b_f_e_o_i$8$(not in LMFDB)
5.2.b_h_g_w_q$8$(not in LMFDB)
5.2.b_j_i_bi_y$8$(not in LMFDB)
5.2.d_d_ac_ak_aq$8$(not in LMFDB)
5.2.d_j_q_be_bo$8$(not in LMFDB)
5.2.d_l_w_bu_cm$8$(not in LMFDB)
5.2.f_r_bo_da_eq$8$(not in LMFDB)
5.2.af_p_abi_cm_adw$12$(not in LMFDB)
5.2.ad_f_ae_e_ae$24$(not in LMFDB)
5.2.ad_j_au_bk_ace$24$(not in LMFDB)
5.2.ad_j_aq_bg_abs$24$(not in LMFDB)
5.2.ab_b_a_e_ae$24$(not in LMFDB)
5.2.ab_d_ac_e_a$24$(not in LMFDB)
5.2.ab_f_ai_m_ay$24$(not in LMFDB)
5.2.ab_f_ae_q_am$24$(not in LMFDB)
5.2.ab_h_ag_y_aq$24$(not in LMFDB)
5.2.b_b_a_e_e$24$(not in LMFDB)
5.2.b_d_c_e_a$24$(not in LMFDB)
5.2.b_f_e_q_m$24$(not in LMFDB)
5.2.b_f_i_m_y$24$(not in LMFDB)
5.2.b_h_g_y_q$24$(not in LMFDB)
5.2.d_f_e_e_e$24$(not in LMFDB)
5.2.d_j_q_bg_bs$24$(not in LMFDB)
5.2.d_j_u_bk_ce$24$(not in LMFDB)