Properties

Label 5.3.al_ch_ahw_tt_abml
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:  $( 1 - 3 x + 3 x^{2} )^{3}( 1 - 2 x + 5 x^{2} - 6 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.254551732336$, $\pm0.538152604671$
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 55223 19054336 4974322171 1376596978337 269372824813568 52353414280000883 12138856505398324611 2966149666575644571904 712088368727173824104663

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -7 7 32 111 363 928 2289 6551 19760 58567

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{3}$
The isogeny class factors as 1.3.ad 3 $\times$ 2.3.ac_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 $\overline{\F}_{3}$
The base change of $A$ to $\F_{3^{6}}$ is 1.729.cc 3 $\times$ 2.729.bk_bww. 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.ah_x_abw_dd_aff$2$(not in LMFDB)
5.3.af_l_am_j_aj$2$(not in LMFDB)
5.3.ab_ab_a_j_aj$2$(not in LMFDB)
5.3.b_ab_a_j_j$2$(not in LMFDB)
5.3.f_l_m_j_j$2$(not in LMFDB)
5.3.h_x_bw_dd_ff$2$(not in LMFDB)
5.3.l_ch_hw_tt_bml$2$(not in LMFDB)
5.3.ai_bj_aee_kb_atk$3$(not in LMFDB)
5.3.af_l_am_j_aj$3$(not in LMFDB)
5.3.af_u_acf_ff_ajs$3$(not in LMFDB)
5.3.ac_f_ag_j_a$3$(not in LMFDB)
5.3.ac_o_ay_dd_aee$3$(not in LMFDB)
5.3.b_ab_a_j_j$3$(not in LMFDB)
5.3.b_i_j_bb_bk$3$(not in LMFDB)
5.3.e_l_y_bt_cu$3$(not in LMFDB)
5.3.h_x_bw_dd_ff$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.3.ah_x_abw_dd_aff$2$(not in LMFDB)
5.3.af_l_am_j_aj$2$(not in LMFDB)
5.3.ab_ab_a_j_aj$2$(not in LMFDB)
5.3.b_ab_a_j_j$2$(not in LMFDB)
5.3.f_l_m_j_j$2$(not in LMFDB)
5.3.h_x_bw_dd_ff$2$(not in LMFDB)
5.3.l_ch_hw_tt_bml$2$(not in LMFDB)
5.3.ai_bj_aee_kb_atk$3$(not in LMFDB)
5.3.af_l_am_j_aj$3$(not in LMFDB)
5.3.af_u_acf_ff_ajs$3$(not in LMFDB)
5.3.ac_f_ag_j_a$3$(not in LMFDB)
5.3.ac_o_ay_dd_aee$3$(not in LMFDB)
5.3.b_ab_a_j_j$3$(not in LMFDB)
5.3.b_i_j_bb_bk$3$(not in LMFDB)
5.3.e_l_y_bt_cu$3$(not in LMFDB)
5.3.h_x_bw_dd_ff$3$(not in LMFDB)
5.3.af_r_abq_dp_agp$4$(not in LMFDB)
5.3.ab_f_ag_v_abb$4$(not in LMFDB)
5.3.b_f_g_v_bb$4$(not in LMFDB)
5.3.f_r_bq_dp_gp$4$(not in LMFDB)
5.3.ae_l_ay_bt_acu$6$(not in LMFDB)
5.3.ab_i_aj_bb_abk$6$(not in LMFDB)
5.3.c_f_g_j_a$6$(not in LMFDB)
5.3.c_o_y_dd_ee$6$(not in LMFDB)
5.3.f_u_cf_ff_js$6$(not in LMFDB)
5.3.i_bj_ee_kb_tk$6$(not in LMFDB)
5.3.ac_f_ap_bb_abt$9$(not in LMFDB)
5.3.ac_f_d_aj_bt$9$(not in LMFDB)
5.3.af_i_d_abh_cu$12$(not in LMFDB)
5.3.ac_c_a_ap_bk$12$(not in LMFDB)
5.3.ac_l_as_cf_acu$12$(not in LMFDB)
5.3.ab_ae_d_d_a$12$(not in LMFDB)
5.3.b_ae_ad_d_a$12$(not in LMFDB)
5.3.c_c_a_ap_abk$12$(not in LMFDB)
5.3.c_l_s_cf_cu$12$(not in LMFDB)
5.3.f_i_ad_abh_acu$12$(not in LMFDB)
5.3.c_f_ad_aj_abt$18$(not in LMFDB)
5.3.c_f_p_bb_bt$18$(not in LMFDB)
5.3.af_o_abb_bz_adm$24$(not in LMFDB)
5.3.ac_i_am_bh_abk$24$(not in LMFDB)
5.3.ab_c_ad_p_as$24$(not in LMFDB)
5.3.b_c_d_p_s$24$(not in LMFDB)
5.3.c_i_m_bh_bk$24$(not in LMFDB)
5.3.f_o_bb_bz_dm$24$(not in LMFDB)