Properties

Label 5.3.ak_bu_aez_kb_arr
Base Field $\F_{3}$
Dimension $5$
Ordinary No
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{3}$
Dimension:  $5$
L-polynomial:  $( 1 - 3 x + 3 x^{2} )^{3}( 1 - x + x^{2} - 3 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.201748855633$, $\pm0.672988571819$
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 36015 12139456 6725621175 1406550257392 251828644515840 58062531125378017 12624038192963754375 2878843942948456493248 707130482388891369043200

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 2 21 134 369 881 2514 6806 19173 58157

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{3}$
The isogeny class factors as 1.3.ad 3 $\times$ 2.3.ab_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.cc 3 $\times$ 2.729.al_abfv. 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.ai_bc_abz_bt_abb$2$(not in LMFDB)
5.3.ae_e_d_j_abt$2$(not in LMFDB)
5.3.ac_ac_j_j_abt$2$(not in LMFDB)
5.3.c_ac_aj_j_bt$2$(not in LMFDB)
5.3.e_e_ad_j_bt$2$(not in LMFDB)
5.3.i_bc_bz_bt_bb$2$(not in LMFDB)
5.3.k_bu_ez_kb_rr$2$(not in LMFDB)
5.3.ah_z_acl_ff_ajs$3$(not in LMFDB)
5.3.ae_e_d_j_abt$3$(not in LMFDB)
5.3.ae_n_abh_cu_aew$3$(not in LMFDB)
5.3.ab_b_ad_j_a$3$(not in LMFDB)
5.3.ab_k_am_bt_acc$3$(not in LMFDB)
5.3.c_ac_aj_j_bt$3$(not in LMFDB)
5.3.c_h_j_s_s$3$(not in LMFDB)
5.3.f_n_v_bb_bk$3$(not in LMFDB)
5.3.i_bc_bz_bt_bb$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.3.ai_bc_abz_bt_abb$2$(not in LMFDB)
5.3.ae_e_d_j_abt$2$(not in LMFDB)
5.3.ac_ac_j_j_abt$2$(not in LMFDB)
5.3.c_ac_aj_j_bt$2$(not in LMFDB)
5.3.e_e_ad_j_bt$2$(not in LMFDB)
5.3.i_bc_bz_bt_bb$2$(not in LMFDB)
5.3.k_bu_ez_kb_rr$2$(not in LMFDB)
5.3.ah_z_acl_ff_ajs$3$(not in LMFDB)
5.3.ae_e_d_j_abt$3$(not in LMFDB)
5.3.ae_n_abh_cu_aew$3$(not in LMFDB)
5.3.ab_b_ad_j_a$3$(not in LMFDB)
5.3.ab_k_am_bt_acc$3$(not in LMFDB)
5.3.c_ac_aj_j_bt$3$(not in LMFDB)
5.3.c_h_j_s_s$3$(not in LMFDB)
5.3.f_n_v_bb_bk$3$(not in LMFDB)
5.3.i_bc_bz_bt_bb$3$(not in LMFDB)
5.3.ae_k_av_bz_adv$4$(not in LMFDB)
5.3.ac_e_ad_p_abb$4$(not in LMFDB)
5.3.c_e_d_p_bb$4$(not in LMFDB)
5.3.e_k_v_bz_dv$4$(not in LMFDB)
5.3.af_n_av_bb_abk$6$(not in LMFDB)
5.3.ac_h_aj_s_as$6$(not in LMFDB)
5.3.b_b_d_j_a$6$(not in LMFDB)
5.3.b_k_m_bt_cc$6$(not in LMFDB)
5.3.e_n_bh_cu_ew$6$(not in LMFDB)
5.3.h_z_cl_ff_js$6$(not in LMFDB)
5.3.ab_b_am_s_aj$9$(not in LMFDB)
5.3.ab_b_g_a_j$9$(not in LMFDB)
5.3.ae_b_p_am_as$12$(not in LMFDB)
5.3.ac_af_p_g_acc$12$(not in LMFDB)
5.3.ab_ac_a_ad_s$12$(not in LMFDB)
5.3.ab_h_aj_bh_abk$12$(not in LMFDB)
5.3.b_ac_a_ad_as$12$(not in LMFDB)
5.3.b_h_j_bh_bk$12$(not in LMFDB)
5.3.c_af_ap_g_cc$12$(not in LMFDB)
5.3.e_b_ap_am_s$12$(not in LMFDB)
5.3.b_b_ag_a_aj$18$(not in LMFDB)
5.3.b_b_m_s_j$18$(not in LMFDB)
5.3.ae_h_aj_be_acu$24$(not in LMFDB)
5.3.ac_b_d_m_abk$24$(not in LMFDB)
5.3.ab_e_ag_v_as$24$(not in LMFDB)
5.3.b_e_g_v_s$24$(not in LMFDB)
5.3.c_b_ad_m_bk$24$(not in LMFDB)
5.3.e_h_j_be_cu$24$(not in LMFDB)