Properties

Label 5.3.ak_bw_afr_mv_axx
Base Field $\F_{3}$
Dimension $5$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian No

Learn more about

Invariants

Base field:  $\F_{3}$
Dimension:  $5$
L-polynomial:  $( 1 - 3 x + 3 x^{2} )^{3}( 1 - x + 3 x^{2} - 3 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.268536328535$, $\pm0.622727850897$
Angle rank:  $2$ (numerical)

This isogeny class is not simple.

Newton polygon

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

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
$A(\F_{q^r})$ 9 52479 14817600 6110707239 1407187137744 237776723251200 52718628794992659 12648916238326409223 2930642897336370619200 707910798769618802690304

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 6 27 126 369 837 2304 6822 19521 58221

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{3}$
The isogeny class factors as 1.3.ad 3 $\times$ 2.3.ab_d 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.acd_deb. 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_be_acr_en_ahh$2$(not in LMFDB)
5.3.ac_a_d_j_abb$2$(not in LMFDB)
5.3.e_g_d_j_bb$2$(not in LMFDB)
5.3.k_bw_fr_mv_xx$2$(not in LMFDB)
5.3.ah_bb_acx_gp_amm$3$(not in LMFDB)
5.3.ae_g_ad_j_abb$3$(not in LMFDB)
5.3.ae_p_abn_dm_agg$3$(not in LMFDB)
5.3.ab_d_ad_j_a$3$(not in LMFDB)
5.3.ab_m_am_cl_acc$3$(not in LMFDB)
5.3.c_a_ad_j_bb$3$(not in LMFDB)
5.3.c_j_p_bk_cc$3$(not in LMFDB)
5.3.f_p_bh_cl_ee$3$(not in LMFDB)
5.3.i_be_cr_en_hh$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.3.ai_be_acr_en_ahh$2$(not in LMFDB)
5.3.ac_a_d_j_abb$2$(not in LMFDB)
5.3.e_g_d_j_bb$2$(not in LMFDB)
5.3.k_bw_fr_mv_xx$2$(not in LMFDB)
5.3.ah_bb_acx_gp_amm$3$(not in LMFDB)
5.3.ae_g_ad_j_abb$3$(not in LMFDB)
5.3.ae_p_abn_dm_agg$3$(not in LMFDB)
5.3.ab_d_ad_j_a$3$(not in LMFDB)
5.3.ab_m_am_cl_acc$3$(not in LMFDB)
5.3.c_a_ad_j_bb$3$(not in LMFDB)
5.3.c_j_p_bk_cc$3$(not in LMFDB)
5.3.f_p_bh_cl_ee$3$(not in LMFDB)
5.3.i_be_cr_en_hh$3$(not in LMFDB)
5.3.ae_m_abb_cl_aen$4$(not in LMFDB)
5.3.ac_g_aj_bb_abt$4$(not in LMFDB)
5.3.c_g_j_bb_bt$4$(not in LMFDB)
5.3.e_m_bb_cl_en$4$(not in LMFDB)
5.3.af_p_abh_cl_aee$6$(not in LMFDB)
5.3.ac_j_ap_bk_acc$6$(not in LMFDB)
5.3.ab_d_ad_j_a$6$(not in LMFDB)
5.3.b_d_d_j_a$6$(not in LMFDB)
5.3.b_m_m_cl_cc$6$(not in LMFDB)
5.3.e_p_bn_dm_gg$6$(not in LMFDB)
5.3.h_bb_cx_gp_mm$6$(not in LMFDB)
5.3.ab_d_am_s_abb$9$(not in LMFDB)
5.3.ab_d_g_a_bb$9$(not in LMFDB)
5.3.ae_d_j_as_s$12$(not in LMFDB)
5.3.ac_ad_j_a_as$12$(not in LMFDB)
5.3.ab_a_a_aj_s$12$(not in LMFDB)
5.3.ab_j_aj_bt_abk$12$(not in LMFDB)
5.3.b_a_a_aj_as$12$(not in LMFDB)
5.3.b_j_j_bt_bk$12$(not in LMFDB)
5.3.c_ad_aj_a_s$12$(not in LMFDB)
5.3.e_d_aj_as_as$12$(not in LMFDB)
5.3.b_d_ag_a_abb$18$(not in LMFDB)
5.3.b_d_m_s_bb$18$(not in LMFDB)
5.3.ae_j_ap_bk_acu$24$(not in LMFDB)
5.3.ac_d_ad_s_abk$24$(not in LMFDB)
5.3.ab_g_ag_bb_as$24$(not in LMFDB)
5.3.b_g_g_bb_s$24$(not in LMFDB)
5.3.c_d_d_s_bk$24$(not in LMFDB)
5.3.e_j_p_bk_cu$24$(not in LMFDB)