Properties

Label 5.3.ak_bv_afi_ll_auu
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:  $( 1 - 3 x + 3 x^{2} )^{3}( 1 - x + 2 x^{2} - 3 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.235082516458$, $\pm0.648854628963$
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
$A(\F_{q^r})$ 8 43904 13346816 6559081984 1434732212968 243767101620224 55176829474152856 12584463561909098496 2879291214277250275328 706286311054803767437184

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 4 24 132 374 856 2402 6788 19176 58084

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{3}$
The isogeny class factors as 1.3.ad 3 $\times$ 2.3.ab_c 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.abk_bas. 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_bd_aci_dd_aee$2$(not in LMFDB)
5.3.ae_f_a_j_abk$2$(not in LMFDB)
5.3.ac_ab_g_j_abk$2$(not in LMFDB)
5.3.c_ab_ag_j_bk$2$(not in LMFDB)
5.3.e_f_a_j_bk$2$(not in LMFDB)
5.3.i_bd_ci_dd_ee$2$(not in LMFDB)
5.3.k_bv_fi_ll_uu$2$(not in LMFDB)
5.3.ah_ba_acr_fx_alc$3$(not in LMFDB)
5.3.ae_f_a_j_abk$3$(not in LMFDB)
5.3.ae_o_abk_dd_afo$3$(not in LMFDB)
5.3.ab_c_ad_j_a$3$(not in LMFDB)
5.3.ab_l_am_cc_acc$3$(not in LMFDB)
5.3.c_ab_ag_j_bk$3$(not in LMFDB)
5.3.c_i_m_bb_bk$3$(not in LMFDB)
5.3.f_o_bb_bt_cu$3$(not in LMFDB)
5.3.i_bd_ci_dd_ee$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.3.ai_bd_aci_dd_aee$2$(not in LMFDB)
5.3.ae_f_a_j_abk$2$(not in LMFDB)
5.3.ac_ab_g_j_abk$2$(not in LMFDB)
5.3.c_ab_ag_j_bk$2$(not in LMFDB)
5.3.e_f_a_j_bk$2$(not in LMFDB)
5.3.i_bd_ci_dd_ee$2$(not in LMFDB)
5.3.k_bv_fi_ll_uu$2$(not in LMFDB)
5.3.ah_ba_acr_fx_alc$3$(not in LMFDB)
5.3.ae_f_a_j_abk$3$(not in LMFDB)
5.3.ae_o_abk_dd_afo$3$(not in LMFDB)
5.3.ab_c_ad_j_a$3$(not in LMFDB)
5.3.ab_l_am_cc_acc$3$(not in LMFDB)
5.3.c_ab_ag_j_bk$3$(not in LMFDB)
5.3.c_i_m_bb_bk$3$(not in LMFDB)
5.3.f_o_bb_bt_cu$3$(not in LMFDB)
5.3.i_bd_ci_dd_ee$3$(not in LMFDB)
5.3.ae_l_ay_cf_aee$4$(not in LMFDB)
5.3.ac_f_ag_v_abk$4$(not in LMFDB)
5.3.c_f_g_v_bk$4$(not in LMFDB)
5.3.e_l_y_cf_ee$4$(not in LMFDB)
5.3.af_o_abb_bt_acu$6$(not in LMFDB)
5.3.ac_i_am_bb_abk$6$(not in LMFDB)
5.3.b_c_d_j_a$6$(not in LMFDB)
5.3.b_l_m_cc_cc$6$(not in LMFDB)
5.3.e_o_bk_dd_fo$6$(not in LMFDB)
5.3.h_ba_cr_fx_lc$6$(not in LMFDB)
5.3.ab_c_am_s_as$9$(not in LMFDB)
5.3.ab_c_g_a_s$9$(not in LMFDB)
5.3.ae_c_m_ap_a$12$(not in LMFDB)
5.3.ac_ae_m_d_abk$12$(not in LMFDB)
5.3.ab_ab_a_ag_s$12$(not in LMFDB)
5.3.ab_i_aj_bn_abk$12$(not in LMFDB)
5.3.b_ab_a_ag_as$12$(not in LMFDB)
5.3.b_i_j_bn_bk$12$(not in LMFDB)
5.3.c_ae_am_d_bk$12$(not in LMFDB)
5.3.e_c_am_ap_a$12$(not in LMFDB)
5.3.b_c_ag_a_as$18$(not in LMFDB)
5.3.b_c_m_s_s$18$(not in LMFDB)
5.3.ae_i_am_bh_acu$24$(not in LMFDB)
5.3.ac_c_a_p_abk$24$(not in LMFDB)
5.3.ab_f_ag_y_as$24$(not in LMFDB)
5.3.b_f_g_y_s$24$(not in LMFDB)
5.3.c_c_a_p_bk$24$(not in LMFDB)
5.3.e_i_m_bh_cu$24$(not in LMFDB)