Properties

Label 5.3.al_cf_ahe_qz_abgf
Base Field $\F_{3}$
Dimension $5$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian No

Learn more about

Invariants

Base field:  $\F_{3}$
Dimension:  $5$
L-polynomial:  $( 1 + x + 3 x^{2} )( 1 - 3 x + 3 x^{2} )^{4}$
Frobenius angles:  $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.593214749339$
Angle rank:  $1$ (numerical)

This isogeny class is not simple.

Newton polygon

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

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 36015 12293120 5143122075 1483234632275 272017438801920 55794332176205705 12998950195866036675 2975480275028737387520 700532673766419908758575

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -7 3 20 111 383 936 2429 6999 19820 57603

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{3}$
The isogeny class factors as 1.3.ad 4 $\times$ 1.3.b 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.ak $\times$ 1.729.cc 4 . 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.an_dd_amg_bhp_acpn$2$(not in LMFDB)
5.3.ah_v_abe_j_bb$2$(not in LMFDB)
5.3.af_j_ag_j_abb$2$(not in LMFDB)
5.3.ab_ad_g_j_abb$2$(not in LMFDB)
5.3.b_ad_ag_j_bb$2$(not in LMFDB)
5.3.f_j_g_j_bb$2$(not in LMFDB)
5.3.h_v_be_j_abb$2$(not in LMFDB)
5.3.l_cf_he_qz_bgf$2$(not in LMFDB)
5.3.n_dd_mg_bhp_cpn$2$(not in LMFDB)
5.3.ai_bh_ads_ir_aqq$3$(not in LMFDB)
5.3.af_j_ag_j_abb$3$(not in LMFDB)
5.3.af_s_abz_en_aii$3$(not in LMFDB)
5.3.ac_d_ag_j_a$3$(not in LMFDB)
5.3.ac_m_ay_cl_aee$3$(not in LMFDB)
5.3.b_ad_ag_j_bb$3$(not in LMFDB)
5.3.b_g_d_j_a$3$(not in LMFDB)
5.3.b_p_m_dm_cc$3$(not in LMFDB)
5.3.e_j_m_j_a$3$(not in LMFDB)
5.3.e_s_bw_en_ii$3$(not in LMFDB)
5.3.h_v_be_j_abb$3$(not in LMFDB)
5.3.h_be_dp_ir_qq$3$(not in LMFDB)
5.3.k_bz_gs_qz_bhg$3$(not in LMFDB)
5.3.n_dd_mg_bhp_cpn$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.3.an_dd_amg_bhp_acpn$2$(not in LMFDB)
5.3.ah_v_abe_j_bb$2$(not in LMFDB)
5.3.af_j_ag_j_abb$2$(not in LMFDB)
5.3.ab_ad_g_j_abb$2$(not in LMFDB)
5.3.b_ad_ag_j_bb$2$(not in LMFDB)
5.3.f_j_g_j_bb$2$(not in LMFDB)
5.3.h_v_be_j_abb$2$(not in LMFDB)
5.3.l_cf_he_qz_bgf$2$(not in LMFDB)
5.3.n_dd_mg_bhp_cpn$2$(not in LMFDB)
5.3.ai_bh_ads_ir_aqq$3$(not in LMFDB)
5.3.af_j_ag_j_abb$3$(not in LMFDB)
5.3.af_s_abz_en_aii$3$(not in LMFDB)
5.3.ac_d_ag_j_a$3$(not in LMFDB)
5.3.ac_m_ay_cl_aee$3$(not in LMFDB)
5.3.b_ad_ag_j_bb$3$(not in LMFDB)
5.3.b_g_d_j_a$3$(not in LMFDB)
5.3.b_p_m_dm_cc$3$(not in LMFDB)
5.3.e_j_m_j_a$3$(not in LMFDB)
5.3.e_s_bw_en_ii$3$(not in LMFDB)
5.3.h_v_be_j_abb$3$(not in LMFDB)
5.3.h_be_dp_ir_qq$3$(not in LMFDB)
5.3.k_bz_gs_qz_bhg$3$(not in LMFDB)
5.3.n_dd_mg_bhp_cpn$3$(not in LMFDB)
5.3.ah_bb_acu_fx_akt$4$(not in LMFDB)
5.3.af_p_abk_dd_afx$4$(not in LMFDB)
5.3.ab_d_a_j_aj$4$(not in LMFDB)
5.3.ab_j_ag_bt_abb$4$(not in LMFDB)
5.3.b_d_a_j_j$4$(not in LMFDB)
5.3.b_j_g_bt_bb$4$(not in LMFDB)
5.3.f_p_bk_dd_fx$4$(not in LMFDB)
5.3.h_bb_cu_fx_kt$4$(not in LMFDB)
5.3.e_m_y_bk_cl$5$(not in LMFDB)
5.3.ak_bz_ags_qz_abhg$6$(not in LMFDB)
5.3.ah_be_adp_ir_aqq$6$(not in LMFDB)
5.3.ae_j_am_j_a$6$(not in LMFDB)
5.3.ae_s_abw_en_aii$6$(not in LMFDB)
5.3.ab_g_ad_j_a$6$(not in LMFDB)
5.3.ab_p_am_dm_acc$6$(not in LMFDB)
5.3.c_d_g_j_a$6$(not in LMFDB)
5.3.c_m_y_cl_ee$6$(not in LMFDB)
5.3.f_s_bz_en_ii$6$(not in LMFDB)
5.3.i_bh_ds_ir_qq$6$(not in LMFDB)
5.3.ab_d_a_aj_j$8$(not in LMFDB)
5.3.b_d_a_aj_aj$8$(not in LMFDB)
5.3.ac_d_ap_bb_abb$9$(not in LMFDB)
5.3.ac_d_d_aj_bb$9$(not in LMFDB)
5.3.b_g_ag_a_acc$9$(not in LMFDB)
5.3.b_g_m_s_cc$9$(not in LMFDB)
5.3.e_j_d_abb_add$9$(not in LMFDB)
5.3.e_j_v_bt_dd$9$(not in LMFDB)
5.3.ae_m_ay_bk_acl$10$(not in LMFDB)
5.3.ac_g_am_s_abt$10$(not in LMFDB)
5.3.c_g_m_s_bt$10$(not in LMFDB)
5.3.ah_s_aj_acl_gy$12$(not in LMFDB)
5.3.af_g_j_abb_bk$12$(not in LMFDB)
5.3.ae_g_a_abb_cu$12$(not in LMFDB)
5.3.ae_p_abk_dd_afo$12$(not in LMFDB)
5.3.ac_a_a_aj_bk$12$(not in LMFDB)
5.3.ac_j_as_bt_acu$12$(not in LMFDB)
5.3.ab_aj_m_s_acc$12$(not in LMFDB)
5.3.ab_ag_j_j_abk$12$(not in LMFDB)
5.3.ab_a_d_aj_a$12$(not in LMFDB)
5.3.ab_d_a_as_s$12$(not in LMFDB)
5.3.ab_m_aj_cl_abk$12$(not in LMFDB)
5.3.b_aj_am_s_cc$12$(not in LMFDB)
5.3.b_ag_aj_j_bk$12$(not in LMFDB)
5.3.b_a_ad_aj_a$12$(not in LMFDB)
5.3.b_d_a_as_as$12$(not in LMFDB)
5.3.b_m_j_cl_bk$12$(not in LMFDB)
5.3.c_a_a_aj_abk$12$(not in LMFDB)
5.3.c_j_s_bt_cu$12$(not in LMFDB)
5.3.e_g_a_abb_acu$12$(not in LMFDB)
5.3.e_p_bk_dd_fo$12$(not in LMFDB)
5.3.f_g_aj_abb_abk$12$(not in LMFDB)
5.3.h_s_j_acl_agy$12$(not in LMFDB)
5.3.ac_g_am_s_abt$15$(not in LMFDB)
5.3.b_a_ad_a_j$15$(not in LMFDB)
5.3.ae_j_av_bt_add$18$(not in LMFDB)
5.3.ae_j_ad_abb_dd$18$(not in LMFDB)
5.3.ab_g_am_s_acc$18$(not in LMFDB)
5.3.ab_g_g_a_cc$18$(not in LMFDB)
5.3.c_d_ad_aj_abb$18$(not in LMFDB)
5.3.c_d_p_bb_bb$18$(not in LMFDB)
5.3.ah_y_abz_dd_aew$24$(not in LMFDB)
5.3.af_m_av_bt_adm$24$(not in LMFDB)
5.3.ae_m_ay_bt_acu$24$(not in LMFDB)
5.3.ac_g_am_bb_abk$24$(not in LMFDB)
5.3.ab_ad_g_a_as$24$(not in LMFDB)
5.3.ab_a_d_j_as$24$(not in LMFDB)
5.3.ab_d_a_s_as$24$(not in LMFDB)
5.3.ab_g_ad_bb_as$24$(not in LMFDB)
5.3.ab_j_ag_bk_as$24$(not in LMFDB)
5.3.b_ad_ag_a_s$24$(not in LMFDB)
5.3.b_a_ad_j_s$24$(not in LMFDB)
5.3.b_d_a_s_s$24$(not in LMFDB)
5.3.b_g_d_bb_s$24$(not in LMFDB)
5.3.b_j_g_bk_s$24$(not in LMFDB)
5.3.c_g_m_bb_bk$24$(not in LMFDB)
5.3.e_m_y_bt_cu$24$(not in LMFDB)
5.3.f_m_v_bt_dm$24$(not in LMFDB)
5.3.h_y_bz_dd_ew$24$(not in LMFDB)
5.3.ab_a_d_a_aj$30$(not in LMFDB)
5.3.ab_d_a_a_a$48$(not in LMFDB)
5.3.b_d_a_a_a$48$(not in LMFDB)
5.3.ab_g_ad_s_aj$60$(not in LMFDB)
5.3.b_g_d_s_j$60$(not in LMFDB)