Properties

Label 5.3.ak_bx_agd_ox_abct
Base Field $\F_{3}$
Dimension $5$
Ordinary No
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

Learn more about

Invariants

Base field:  $\F_{3}$
Dimension:  $5$
L-polynomial:  $( 1 - 3 x + 3 x^{2} )^{2}( 1 - 4 x + 10 x^{2} - 21 x^{3} + 30 x^{4} - 36 x^{5} + 27 x^{6} )$
Frobenius angles:  $\pm0.0145064862012$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.383559653096$, $\pm0.564732805964$
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
$A(\F_{q^r})$ 7 44247 11398576 2968663971 907636535197 217880406261504 50713356559716571 12492634994784032907 2962941353177669635072 699162416223096543672927

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 8 21 68 264 773 2220 6740 19740 57488

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{3}$
The isogeny class factors as 1.3.ad 2 $\times$ 3.3.ae_k_av 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 $\overline{\F}_{3}$
The base change of $A$ to $\F_{3^{6}}$ is 1.729.cc 2 $\times$ 3.729.acn_djq_adrer. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{3^{6}}$.
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
5.3.ac_b_d_aj_bb$2$(not in LMFDB)
5.3.e_h_j_j_j$2$(not in LMFDB)
5.3.k_bx_gd_ox_bct$2$(not in LMFDB)
5.3.ah_bc_adg_hq_aoo$3$(not in LMFDB)
5.3.ae_b_p_aj_abb$3$(not in LMFDB)
5.3.ae_h_aj_j_aj$3$(not in LMFDB)
5.3.ae_h_aj_bb_acl$3$(not in LMFDB)
5.3.ae_q_abt_dv_ahq$3$(not in LMFDB)
5.3.ab_ac_a_a_s$3$(not in LMFDB)
5.3.ab_e_ag_a_as$3$(not in LMFDB)
5.3.ab_e_ag_s_as$3$(not in LMFDB)
5.3.c_af_ap_j_cl$3$(not in LMFDB)
5.3.c_b_ad_aj_abb$3$(not in LMFDB)
5.3.c_b_ad_j_bb$3$(not in LMFDB)
5.3.c_e_d_aj_as$3$(not in LMFDB)
5.3.c_k_p_bt_cc$3$(not in LMFDB)
5.3.f_k_g_as_acc$3$(not in LMFDB)
5.3.f_q_bk_cu_ew$3$(not in LMFDB)
5.3.i_z_bb_abt_agp$3$(not in LMFDB)
5.3.i_bf_cx_ff_ir$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.3.ac_b_d_aj_bb$2$(not in LMFDB)
5.3.e_h_j_j_j$2$(not in LMFDB)
5.3.k_bx_gd_ox_bct$2$(not in LMFDB)
5.3.ah_bc_adg_hq_aoo$3$(not in LMFDB)
5.3.ae_b_p_aj_abb$3$(not in LMFDB)
5.3.ae_h_aj_j_aj$3$(not in LMFDB)
5.3.ae_h_aj_bb_acl$3$(not in LMFDB)
5.3.ae_q_abt_dv_ahq$3$(not in LMFDB)
5.3.ab_ac_a_a_s$3$(not in LMFDB)
5.3.ab_e_ag_a_as$3$(not in LMFDB)
5.3.ab_e_ag_s_as$3$(not in LMFDB)
5.3.c_af_ap_j_cl$3$(not in LMFDB)
5.3.c_b_ad_aj_abb$3$(not in LMFDB)
5.3.c_b_ad_j_bb$3$(not in LMFDB)
5.3.c_e_d_aj_as$3$(not in LMFDB)
5.3.c_k_p_bt_cc$3$(not in LMFDB)
5.3.f_k_g_as_acc$3$(not in LMFDB)
5.3.f_q_bk_cu_ew$3$(not in LMFDB)
5.3.i_z_bb_abt_agp$3$(not in LMFDB)
5.3.i_bf_cx_ff_ir$3$(not in LMFDB)
5.3.ae_n_abh_cr_aff$4$(not in LMFDB)
5.3.e_n_bh_cr_ff$4$(not in LMFDB)
5.3.ai_z_abb_abt_gp$6$(not in LMFDB)
5.3.ai_bf_acx_ff_air$6$(not in LMFDB)
5.3.af_k_ag_as_cc$6$(not in LMFDB)
5.3.af_q_abk_cu_aew$6$(not in LMFDB)
5.3.ac_af_p_j_acl$6$(not in LMFDB)
5.3.ac_b_d_j_abb$6$(not in LMFDB)
5.3.ac_e_ad_aj_s$6$(not in LMFDB)
5.3.ac_k_ap_bt_acc$6$(not in LMFDB)
5.3.b_ac_a_a_as$6$(not in LMFDB)
5.3.b_e_g_a_s$6$(not in LMFDB)
5.3.b_e_g_s_s$6$(not in LMFDB)
5.3.c_af_ap_j_cl$6$(not in LMFDB)
5.3.e_b_ap_aj_bb$6$(not in LMFDB)
5.3.e_h_j_bb_cl$6$(not in LMFDB)
5.3.e_q_bt_dv_hq$6$(not in LMFDB)
5.3.h_bc_dg_hq_oo$6$(not in LMFDB)
5.3.ae_e_d_av_cc$12$(not in LMFDB)
5.3.ac_ai_v_p_adm$12$(not in LMFDB)
5.3.ac_ac_j_ad_as$12$(not in LMFDB)
5.3.ac_b_d_ad_aj$12$(not in LMFDB)
5.3.ac_h_aj_bh_abt$12$(not in LMFDB)
5.3.c_ai_av_p_dm$12$(not in LMFDB)
5.3.c_ac_aj_ad_s$12$(not in LMFDB)
5.3.c_b_ad_ad_j$12$(not in LMFDB)
5.3.c_h_j_bh_bt$12$(not in LMFDB)
5.3.e_e_ad_av_acc$12$(not in LMFDB)
5.3.ae_k_av_bn_acu$24$(not in LMFDB)
5.3.ac_ac_j_d_abk$24$(not in LMFDB)
5.3.ac_e_ad_v_abk$24$(not in LMFDB)
5.3.c_ac_aj_d_bk$24$(not in LMFDB)
5.3.c_e_d_v_bk$24$(not in LMFDB)
5.3.e_k_v_bn_cu$24$(not in LMFDB)