Properties

Label 5.3.al_ce_agv_pp_abdc
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:  $( 1 - 3 x + 3 x^{2} )^{3}( 1 - 2 x + 2 x^{2} - 6 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.116139763599$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.616139763599$
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
$A(\F_{q^r})$ 4 27440 9571072 4822854400 1374148969484 256327090503680 56541384167257364 13238272102480588800 2990708809374622556416 709094956080155504846000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -7 1 14 105 363 892 2457 7121 19922 58321

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{3}$
The isogeny class factors as 1.3.ad 3 $\times$ 2.3.ac_c 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 $\F_{3^{12}}$ is 1.531441.acec 3 $\times$ 1.531441.sk 2 . The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{3^{12}}$.
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
5.3.ah_u_av_abb_ee$2$(not in LMFDB)
5.3.af_i_ad_j_abk$2$(not in LMFDB)
5.3.ab_ae_j_j_abk$2$(not in LMFDB)
5.3.b_ae_aj_j_bk$2$(not in LMFDB)
5.3.f_i_d_j_bk$2$(not in LMFDB)
5.3.h_u_v_abb_aee$2$(not in LMFDB)
5.3.l_ce_gv_pp_bdc$2$(not in LMFDB)
5.3.ai_bg_adm_hz_apg$3$(not in LMFDB)
5.3.af_i_ad_j_abk$3$(not in LMFDB)
5.3.af_r_abw_ee_ahq$3$(not in LMFDB)
5.3.ac_c_ag_j_a$3$(not in LMFDB)
5.3.ac_l_ay_cc_aee$3$(not in LMFDB)
5.3.b_ae_aj_j_bk$3$(not in LMFDB)
5.3.b_f_a_a_as$3$(not in LMFDB)
5.3.e_i_g_aj_abk$3$(not in LMFDB)
5.3.h_u_v_abb_aee$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.3.ah_u_av_abb_ee$2$(not in LMFDB)
5.3.af_i_ad_j_abk$2$(not in LMFDB)
5.3.ab_ae_j_j_abk$2$(not in LMFDB)
5.3.b_ae_aj_j_bk$2$(not in LMFDB)
5.3.f_i_d_j_bk$2$(not in LMFDB)
5.3.h_u_v_abb_aee$2$(not in LMFDB)
5.3.l_ce_gv_pp_bdc$2$(not in LMFDB)
5.3.ai_bg_adm_hz_apg$3$(not in LMFDB)
5.3.af_i_ad_j_abk$3$(not in LMFDB)
5.3.af_r_abw_ee_ahq$3$(not in LMFDB)
5.3.ac_c_ag_j_a$3$(not in LMFDB)
5.3.ac_l_ay_cc_aee$3$(not in LMFDB)
5.3.b_ae_aj_j_bk$3$(not in LMFDB)
5.3.b_f_a_a_as$3$(not in LMFDB)
5.3.e_i_g_aj_abk$3$(not in LMFDB)
5.3.h_u_v_abb_aee$3$(not in LMFDB)
5.3.af_o_abh_cx_afo$4$(not in LMFDB)
5.3.ab_c_d_d_a$4$(not in LMFDB)
5.3.b_c_ad_d_a$4$(not in LMFDB)
5.3.f_o_bh_cx_fo$4$(not in LMFDB)
5.3.ae_i_ag_aj_bk$6$(not in LMFDB)
5.3.ab_f_a_a_s$6$(not in LMFDB)
5.3.c_c_g_j_a$6$(not in LMFDB)
5.3.c_l_y_cc_ee$6$(not in LMFDB)
5.3.f_r_bw_ee_hq$6$(not in LMFDB)
5.3.i_bg_dm_hz_pg$6$(not in LMFDB)
5.3.aj_bg_abt_abb_gg$8$(not in LMFDB)
5.3.aj_bo_aen_kb_ass$8$(not in LMFDB)
5.3.ad_ae_v_j_adm$8$(not in LMFDB)
5.3.ad_c_d_d_as$8$(not in LMFDB)
5.3.ad_e_ad_j_as$8$(not in LMFDB)
5.3.ad_k_av_bz_adm$8$(not in LMFDB)
5.3.d_ae_av_j_dm$8$(not in LMFDB)
5.3.d_c_ad_d_s$8$(not in LMFDB)
5.3.d_e_d_j_s$8$(not in LMFDB)
5.3.d_k_v_bz_dm$8$(not in LMFDB)
5.3.j_bg_bt_abb_agg$8$(not in LMFDB)
5.3.j_bo_en_kb_ss$8$(not in LMFDB)
5.3.ac_c_ap_bb_as$9$(not in LMFDB)
5.3.ac_c_d_aj_s$9$(not in LMFDB)
5.3.af_f_m_ay_s$12$(not in LMFDB)
5.3.ac_ab_a_ag_bk$12$(not in LMFDB)
5.3.ac_i_as_bn_acu$12$(not in LMFDB)
5.3.ab_ah_m_m_acc$12$(not in LMFDB)
5.3.b_ah_am_m_cc$12$(not in LMFDB)
5.3.c_ab_a_ag_abk$12$(not in LMFDB)
5.3.c_i_s_bn_cu$12$(not in LMFDB)
5.3.f_f_am_ay_as$12$(not in LMFDB)
5.3.c_c_ad_aj_as$18$(not in LMFDB)
5.3.c_c_p_bb_s$18$(not in LMFDB)
5.3.ag_o_am_aj_bk$24$(not in LMFDB)
5.3.ag_w_aci_ff_ajs$24$(not in LMFDB)
5.3.af_l_as_bq_adm$24$(not in LMFDB)
5.3.ad_ah_be_m_aew$24$(not in LMFDB)
5.3.ad_ab_m_g_acc$24$(not in LMFDB)
5.3.ad_b_g_am_s$24$(not in LMFDB)
5.3.ad_f_ag_a_s$24$(not in LMFDB)
5.3.ad_h_am_be_acc$24$(not in LMFDB)
5.3.ad_n_abe_cu_aew$24$(not in LMFDB)
5.3.ac_f_am_y_abk$24$(not in LMFDB)
5.3.ab_ab_g_g_as$24$(not in LMFDB)
5.3.a_ah_a_m_a$24$(not in LMFDB)
5.3.a_ae_a_j_a$24$(not in LMFDB)
5.3.a_ab_a_g_a$24$(not in LMFDB)
5.3.a_b_a_am_a$24$(not in LMFDB)
5.3.a_c_a_d_a$24$(not in LMFDB)
5.3.a_e_a_j_a$24$(not in LMFDB)
5.3.a_f_a_a_a$24$(not in LMFDB)
5.3.a_h_a_be_a$24$(not in LMFDB)
5.3.a_k_a_bz_a$24$(not in LMFDB)
5.3.a_n_a_cu_a$24$(not in LMFDB)
5.3.b_ab_ag_g_s$24$(not in LMFDB)
5.3.c_f_m_y_bk$24$(not in LMFDB)
5.3.d_ah_abe_m_ew$24$(not in LMFDB)
5.3.d_ab_am_g_cc$24$(not in LMFDB)
5.3.d_b_ag_am_as$24$(not in LMFDB)
5.3.d_f_g_a_as$24$(not in LMFDB)
5.3.d_h_m_be_cc$24$(not in LMFDB)
5.3.d_n_be_cu_ew$24$(not in LMFDB)
5.3.f_l_s_bq_dm$24$(not in LMFDB)
5.3.g_o_m_aj_abk$24$(not in LMFDB)
5.3.g_w_ci_ff_js$24$(not in LMFDB)
5.3.a_ae_aj_j_bk$72$(not in LMFDB)
5.3.a_ae_j_j_abk$72$(not in LMFDB)
5.3.a_e_aj_j_abk$72$(not in LMFDB)
5.3.a_e_j_j_bk$72$(not in LMFDB)