Properties

Label 5.3.ak_bx_agc_or_abce
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:  $( 1 - 3 x + 3 x^{2} )^{2}( 1 - 4 x + 10 x^{2} - 20 x^{3} + 30 x^{4} - 36 x^{5} + 27 x^{6} )$
Frobenius angles:  $\pm0.0844416807585$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.360432408976$, $\pm0.575465777728$
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
$A(\F_{q^r})$ 8 50176 13121024 3697168384 1036176718888 226476012077056 52415886206779096 13023712682309009408 3052799073160079161856 711112415711367293510656

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 8 24 84 294 800 2290 7012 20328 58488

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{3}$
The isogeny class factors as 1.3.ad 2 $\times$ 3.3.ae_k_au 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 2 $\times$ 3.729.abm_cpz_adepg. 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.ac_b_c_ad_m$2$(not in LMFDB)
5.3.e_h_i_j_m$2$(not in LMFDB)
5.3.k_bx_gc_or_bce$2$(not in LMFDB)
5.3.ah_bc_adf_hn_aoi$3$(not in LMFDB)
5.3.ae_h_ai_j_am$3$(not in LMFDB)
5.3.ae_q_abs_dv_ahk$3$(not in LMFDB)
5.3.ab_e_af_d_am$3$(not in LMFDB)
5.3.c_b_ac_ad_am$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.3.ac_b_c_ad_m$2$(not in LMFDB)
5.3.e_h_i_j_m$2$(not in LMFDB)
5.3.k_bx_gc_or_bce$2$(not in LMFDB)
5.3.ah_bc_adf_hn_aoi$3$(not in LMFDB)
5.3.ae_h_ai_j_am$3$(not in LMFDB)
5.3.ae_q_abs_dv_ahk$3$(not in LMFDB)
5.3.ab_e_af_d_am$3$(not in LMFDB)
5.3.c_b_ac_ad_am$3$(not in LMFDB)
5.3.ae_n_abg_cr_afc$4$(not in LMFDB)
5.3.e_n_bg_cr_fc$4$(not in LMFDB)
5.3.ah_bc_adf_hn_aoi$6$(not in LMFDB)
5.3.b_e_f_d_m$6$(not in LMFDB)
5.3.e_q_bs_dv_hk$6$(not in LMFDB)
5.3.h_bc_df_hn_oi$6$(not in LMFDB)
5.3.ae_e_e_av_bw$12$(not in LMFDB)
5.3.e_e_ae_av_abw$12$(not in LMFDB)
5.3.ae_k_au_bn_acu$24$(not in LMFDB)
5.3.e_k_u_bn_cu$24$(not in LMFDB)