Properties

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

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Invariants

Base field:  $\F_{3}$
Dimension:  $5$
L-polynomial:  $( 1 - 2 x + 3 x^{2} )( 1 - 3 x + 3 x^{2} )^{2}( 1 - 3 x + 7 x^{2} - 9 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.227267020856$, $\pm0.304086723985$, $\pm0.464830336654$
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
$A(\F_{q^r})$ 10 85260 31430560 5187218400 1101908764000 244394982558720 52712767854495010 11956788913150972800 2906332605830394821920 716644154693490866304000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -7 11 47 115 308 857 2303 6451 19361 58946

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_h 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.cn_dov. 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_z_acj_et_aio$2$(not in LMFDB)
5.3.af_n_ax_bn_aco$2$(not in LMFDB)
5.3.af_n_ar_j_g$2$(not in LMFDB)
5.3.ab_b_ah_p_ag$2$(not in LMFDB)
5.3.ab_b_ab_j_ag$2$(not in LMFDB)
5.3.b_b_b_j_g$2$(not in LMFDB)
5.3.b_b_h_p_g$2$(not in LMFDB)
5.3.f_n_r_j_ag$2$(not in LMFDB)
5.3.f_n_x_bn_co$2$(not in LMFDB)
5.3.h_z_cj_et_io$2$(not in LMFDB)
5.3.l_cj_in_wh_bsc$2$(not in LMFDB)
5.3.ai_bl_aep_li_avy$3$(not in LMFDB)
5.3.af_n_ar_j_g$3$(not in LMFDB)
5.3.af_w_ack_fx_akw$3$(not in LMFDB)
5.3.ac_h_af_m_g$3$(not in LMFDB)
5.3.b_b_h_p_g$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.3.ah_z_acj_et_aio$2$(not in LMFDB)
5.3.af_n_ax_bn_aco$2$(not in LMFDB)
5.3.af_n_ar_j_g$2$(not in LMFDB)
5.3.ab_b_ah_p_ag$2$(not in LMFDB)
5.3.ab_b_ab_j_ag$2$(not in LMFDB)
5.3.b_b_b_j_g$2$(not in LMFDB)
5.3.b_b_h_p_g$2$(not in LMFDB)
5.3.f_n_r_j_ag$2$(not in LMFDB)
5.3.f_n_x_bn_co$2$(not in LMFDB)
5.3.h_z_cj_et_io$2$(not in LMFDB)
5.3.l_cj_in_wh_bsc$2$(not in LMFDB)
5.3.ai_bl_aep_li_avy$3$(not in LMFDB)
5.3.af_n_ar_j_g$3$(not in LMFDB)
5.3.af_w_ack_fx_akw$3$(not in LMFDB)
5.3.ac_h_af_m_g$3$(not in LMFDB)
5.3.b_b_h_p_g$3$(not in LMFDB)
5.3.af_t_abv_eb_ahe$4$(not in LMFDB)
5.3.ab_h_ah_bh_abe$4$(not in LMFDB)
5.3.b_h_h_bh_be$4$(not in LMFDB)
5.3.f_t_bv_eb_he$4$(not in LMFDB)
5.3.ae_n_abf_co_aek$6$(not in LMFDB)
5.3.ac_h_al_y_abe$6$(not in LMFDB)
5.3.ab_k_ak_bt_abq$6$(not in LMFDB)
5.3.b_k_k_bt_bq$6$(not in LMFDB)
5.3.c_h_f_m_ag$6$(not in LMFDB)
5.3.c_h_l_y_be$6$(not in LMFDB)
5.3.e_n_bf_co_ek$6$(not in LMFDB)
5.3.f_w_ck_fx_kw$6$(not in LMFDB)
5.3.i_bl_ep_li_vy$6$(not in LMFDB)
5.3.af_k_ac_abn_dy$12$(not in LMFDB)
5.3.ab_ac_c_ad_g$12$(not in LMFDB)
5.3.b_ac_ac_ad_ag$12$(not in LMFDB)
5.3.f_k_c_abn_ady$12$(not in LMFDB)
5.3.af_q_abg_cf_adm$24$(not in LMFDB)
5.3.ab_e_ae_v_as$24$(not in LMFDB)
5.3.b_e_e_v_s$24$(not in LMFDB)
5.3.f_q_bg_cf_dm$24$(not in LMFDB)