Properties

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

Learn more about

Invariants

Base field:  $\F_{3}$
Dimension:  $5$
L-polynomial:  $( 1 - 2 x + 3 x^{2} )( 1 - 3 x + 3 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 9 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.0975263560046$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.304086723985$, $\pm0.527857038681$
Angle rank:  $3$ (numerical)

This isogeny class is not simple.

Newton polygon

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1/2, 1/2, 1/2, 1/2, 1, 1, 1]$

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
$A(\F_{q^r})$ 6 47628 16355808 3927976416 1109870943456 243046260108288 51707352610402278 12401985480130786176 3053557949789098356192 727582255708463853401088

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -7 7 29 91 308 853 2261 6691 20333 59842

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{3}$
The isogeny class factors as 1.3.ad 2 $\times$ 1.3.ac $\times$ 2.3.ad_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.abu $\times$ 1.729.cc 2 $\times$ 2.729.cj_ddt. 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_acb_eh_aic$2$(not in LMFDB)
5.3.af_l_an_j_ag$2$(not in LMFDB)
5.3.af_l_ah_av_co$2$(not in LMFDB)
5.3.ab_ab_af_j_g$2$(not in LMFDB)
5.3.ab_ab_b_d_g$2$(not in LMFDB)
5.3.b_ab_ab_d_ag$2$(not in LMFDB)
5.3.b_ab_f_j_ag$2$(not in LMFDB)
5.3.f_l_h_av_aco$2$(not in LMFDB)
5.3.f_l_n_j_g$2$(not in LMFDB)
5.3.h_x_cb_eh_ic$2$(not in LMFDB)
5.3.l_ch_hx_tz_bna$2$(not in LMFDB)
5.3.ai_bj_aef_ke_atq$3$(not in LMFDB)
5.3.af_l_an_j_ag$3$(not in LMFDB)
5.3.af_u_acg_ff_ajy$3$(not in LMFDB)
5.3.ac_f_ah_g_ag$3$(not in LMFDB)
5.3.b_ab_ab_d_ag$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.3.ah_x_acb_eh_aic$2$(not in LMFDB)
5.3.af_l_an_j_ag$2$(not in LMFDB)
5.3.af_l_ah_av_co$2$(not in LMFDB)
5.3.ab_ab_af_j_g$2$(not in LMFDB)
5.3.ab_ab_b_d_g$2$(not in LMFDB)
5.3.b_ab_ab_d_ag$2$(not in LMFDB)
5.3.b_ab_f_j_ag$2$(not in LMFDB)
5.3.f_l_h_av_aco$2$(not in LMFDB)
5.3.f_l_n_j_g$2$(not in LMFDB)
5.3.h_x_cb_eh_ic$2$(not in LMFDB)
5.3.l_ch_hx_tz_bna$2$(not in LMFDB)
5.3.ai_bj_aef_ke_atq$3$(not in LMFDB)
5.3.af_l_an_j_ag$3$(not in LMFDB)
5.3.af_u_acg_ff_ajy$3$(not in LMFDB)
5.3.ac_f_ah_g_ag$3$(not in LMFDB)
5.3.b_ab_ab_d_ag$3$(not in LMFDB)
5.3.af_r_abr_dp_ags$4$(not in LMFDB)
5.3.ab_f_al_v_abq$4$(not in LMFDB)
5.3.b_f_l_v_bq$4$(not in LMFDB)
5.3.f_r_br_dp_gs$4$(not in LMFDB)
5.3.ae_l_abd_ci_ady$6$(not in LMFDB)
5.3.ac_f_ab_ag_be$6$(not in LMFDB)
5.3.ab_i_ao_bb_aco$6$(not in LMFDB)
5.3.b_i_o_bb_co$6$(not in LMFDB)
5.3.c_f_b_ag_abe$6$(not in LMFDB)
5.3.c_f_h_g_g$6$(not in LMFDB)
5.3.e_l_bd_ci_dy$6$(not in LMFDB)
5.3.f_u_cg_ff_jy$6$(not in LMFDB)
5.3.i_bj_ef_ke_tq$6$(not in LMFDB)
5.3.af_i_c_abh_da$12$(not in LMFDB)
5.3.ab_ae_ac_d_be$12$(not in LMFDB)
5.3.b_ae_c_d_abe$12$(not in LMFDB)
5.3.f_i_ac_abh_ada$12$(not in LMFDB)
5.3.af_o_abc_bz_adm$24$(not in LMFDB)
5.3.ab_c_ai_p_as$24$(not in LMFDB)
5.3.b_c_i_p_s$24$(not in LMFDB)
5.3.f_o_bc_bz_dm$24$(not in LMFDB)