Properties

Label 5.3.ak_bs_aeh_hh_all
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:  $\pm0.126866938441$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.718153680921$
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
$A(\F_{q^r})$ 5 22295 9988160 6122764375 1202111664400 259384684482560 60645830392084495 12711983771875854375 2988178715703504464960 717949120226839108025600

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 -2 15 126 329 901 2612 6854 19905 59053

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{3}$
The isogeny class factors as 1.3.ad 3 $\times$ 2.3.ab_ab 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.j_jt. 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_ba_abh_abb_ff$2$(not in LMFDB)
5.3.ac_ae_p_j_acl$2$(not in LMFDB)
5.3.e_c_aj_j_cl$2$(not in LMFDB)
5.3.k_bs_eh_hh_ll$2$(not in LMFDB)
5.3.ah_x_abz_dv_agy$3$(not in LMFDB)
5.3.ae_c_j_j_acl$3$(not in LMFDB)
5.3.ae_l_abb_cc_adm$3$(not in LMFDB)
5.3.ab_ab_ad_j_a$3$(not in LMFDB)
5.3.ab_i_am_bb_acc$3$(not in LMFDB)
5.3.c_ae_ap_j_cl$3$(not in LMFDB)
5.3.c_f_d_a_as$3$(not in LMFDB)
5.3.f_l_j_aj_abk$3$(not in LMFDB)
5.3.i_ba_bh_abb_aff$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.3.ai_ba_abh_abb_ff$2$(not in LMFDB)
5.3.ac_ae_p_j_acl$2$(not in LMFDB)
5.3.e_c_aj_j_cl$2$(not in LMFDB)
5.3.k_bs_eh_hh_ll$2$(not in LMFDB)
5.3.ah_x_abz_dv_agy$3$(not in LMFDB)
5.3.ae_c_j_j_acl$3$(not in LMFDB)
5.3.ae_l_abb_cc_adm$3$(not in LMFDB)
5.3.ab_ab_ad_j_a$3$(not in LMFDB)
5.3.ab_i_am_bb_acc$3$(not in LMFDB)
5.3.c_ae_ap_j_cl$3$(not in LMFDB)
5.3.c_f_d_a_as$3$(not in LMFDB)
5.3.f_l_j_aj_abk$3$(not in LMFDB)
5.3.i_ba_bh_abb_aff$3$(not in LMFDB)
5.3.ae_i_ap_bn_add$4$(not in LMFDB)
5.3.ac_c_d_d_aj$4$(not in LMFDB)
5.3.c_c_ad_d_j$4$(not in LMFDB)
5.3.e_i_p_bn_dd$4$(not in LMFDB)
5.3.af_l_aj_aj_bk$6$(not in LMFDB)
5.3.ac_f_ad_a_s$6$(not in LMFDB)
5.3.b_ab_d_j_a$6$(not in LMFDB)
5.3.b_i_m_bb_cc$6$(not in LMFDB)
5.3.c_f_d_a_as$6$(not in LMFDB)
5.3.e_l_bb_cc_dm$6$(not in LMFDB)
5.3.h_x_bz_dv_gy$6$(not in LMFDB)
5.3.ab_ab_am_s_j$9$(not in LMFDB)
5.3.ab_ab_g_a_aj$9$(not in LMFDB)
5.3.ae_ab_v_ag_acc$12$(not in LMFDB)
5.3.ac_ah_v_m_adm$12$(not in LMFDB)
5.3.ab_ae_a_d_s$12$(not in LMFDB)
5.3.ab_f_aj_v_abk$12$(not in LMFDB)
5.3.b_ae_a_d_as$12$(not in LMFDB)
5.3.b_f_j_v_bk$12$(not in LMFDB)
5.3.c_ah_av_m_dm$12$(not in LMFDB)
5.3.e_ab_av_ag_cc$12$(not in LMFDB)
5.3.b_ab_ag_a_j$18$(not in LMFDB)
5.3.b_ab_m_s_aj$18$(not in LMFDB)
5.3.ae_f_ad_y_acu$24$(not in LMFDB)
5.3.ac_ab_j_g_abk$24$(not in LMFDB)
5.3.ab_c_ag_p_as$24$(not in LMFDB)
5.3.b_c_g_p_s$24$(not in LMFDB)
5.3.c_ab_aj_g_bk$24$(not in LMFDB)
5.3.e_f_d_y_cu$24$(not in LMFDB)