Properties

Label 4.3.aj_bp_aeq_jm
Base Field $\F_{3}$
Dimension $4$
Ordinary No
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{3}$
Dimension:  $4$
L-polynomial:  $( 1 - 2 x + 3 x^{2} )( 1 - x + 3 x^{2} )( 1 - 3 x + 3 x^{2} )^{2}$
Frobenius angles:  $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.304086723985$, $\pm0.406785250661$
Angle rank:  $2$ (numerical)

This isogeny class is not simple.

Newton polygon

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

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
$A(\F_{q^r})$ 6 8820 1072512 59623200 3785589786 302705786880 24576432300762 1922914262505600 150526973078358912 12059264472339338100

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 11 46 107 265 782 2347 6803 19738 58571

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{3}$
The isogeny class factors as 1.3.ad 2 $\times$ 1.3.ac $\times$ 1.3.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.abu $\times$ 1.729.ak $\times$ 1.729.cc 2 . 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
4.3.ah_z_aci_ek$2$(not in LMFDB)
4.3.af_n_ay_bq$2$(not in LMFDB)
4.3.ad_f_am_be$2$(not in LMFDB)
4.3.ab_b_a_g$2$(not in LMFDB)
4.3.b_b_a_g$2$(not in LMFDB)
4.3.d_f_a_ag$2$(not in LMFDB)
4.3.f_n_y_bq$2$(not in LMFDB)
4.3.h_z_ci_ek$2$(not in LMFDB)
4.3.j_bp_eq_jm$2$(not in LMFDB)
4.3.ag_x_aci_eq$3$(not in LMFDB)
4.3.ad_f_a_ag$3$(not in LMFDB)
4.3.ad_o_abb_co$3$(not in LMFDB)
4.3.a_f_g_m$3$(not in LMFDB)
4.3.d_f_m_be$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
4.3.ah_z_aci_ek$2$(not in LMFDB)
4.3.af_n_ay_bq$2$(not in LMFDB)
4.3.ad_f_am_be$2$(not in LMFDB)
4.3.ab_b_a_g$2$(not in LMFDB)
4.3.b_b_a_g$2$(not in LMFDB)
4.3.d_f_a_ag$2$(not in LMFDB)
4.3.f_n_y_bq$2$(not in LMFDB)
4.3.h_z_ci_ek$2$(not in LMFDB)
4.3.j_bp_eq_jm$2$(not in LMFDB)
4.3.ag_x_aci_eq$3$(not in LMFDB)
4.3.ad_f_a_ag$3$(not in LMFDB)
4.3.ad_o_abb_co$3$(not in LMFDB)
4.3.a_f_g_m$3$(not in LMFDB)
4.3.d_f_m_be$3$(not in LMFDB)
4.3.ad_l_as_bq$4$(not in LMFDB)
4.3.ab_h_ag_be$4$(not in LMFDB)
4.3.b_h_g_be$4$(not in LMFDB)
4.3.d_l_s_bq$4$(not in LMFDB)
4.3.ae_n_abe_ci$6$(not in LMFDB)
4.3.ad_o_abb_co$6$(not in LMFDB)
4.3.ac_h_am_y$6$(not in LMFDB)
4.3.ab_k_aj_bq$6$(not in LMFDB)
4.3.a_f_ag_m$6$(not in LMFDB)
4.3.b_k_j_bq$6$(not in LMFDB)
4.3.c_h_m_y$6$(not in LMFDB)
4.3.d_o_bb_co$6$(not in LMFDB)
4.3.e_n_be_ci$6$(not in LMFDB)
4.3.g_x_ci_eq$6$(not in LMFDB)
4.3.ad_c_j_abe$12$(not in LMFDB)
4.3.ab_ac_d_ag$12$(not in LMFDB)
4.3.b_ac_ad_ag$12$(not in LMFDB)
4.3.d_c_aj_abe$12$(not in LMFDB)
4.3.ad_i_aj_s$24$(not in LMFDB)
4.3.ab_e_ad_s$24$(not in LMFDB)
4.3.b_e_d_s$24$(not in LMFDB)
4.3.d_i_j_s$24$(not in LMFDB)