Properties

Label 4.3.ah_v_abk_cc
Base Field $\F_{3}$
Dimension $4$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{3}$
Dimension:  $4$
L-polynomial:  $( 1 + 2 x + 3 x^{2} )( 1 - 3 x + 3 x^{2} )^{3}$
Frobenius angles:  $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.695913276015$
Angle rank:  $1$ (numerical)

This isogeny class is not simple.

Newton polygon

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

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 4116 395136 72342816 4896017706 329612967936 26564029141866 1913695797127296 148676055648494976 12107028012374894676

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 3 18 123 327 846 2517 6771 19494 58803

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{3}$
The isogeny class factors as 1.3.ad 3 $\times$ 1.3.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.abu $\times$ 1.729.cc 3 . 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.al_cf_agy_oo$2$(not in LMFDB)
4.3.af_j_a_as$2$(not in LMFDB)
4.3.ab_ad_a_s$2$(not in LMFDB)
4.3.b_ad_a_s$2$(not in LMFDB)
4.3.f_j_a_as$2$(not in LMFDB)
4.3.h_v_bk_cc$2$(not in LMFDB)
4.3.l_cf_gy_oo$2$(not in LMFDB)
4.3.ae_j_as_bk$3$(not in LMFDB)
4.3.ab_ad_a_s$3$(not in LMFDB)
4.3.ab_g_aj_s$3$(not in LMFDB)
4.3.c_d_a_a$3$(not in LMFDB)
4.3.c_m_s_cc$3$(not in LMFDB)
4.3.f_j_a_as$3$(not in LMFDB)
4.3.f_s_bt_dm$3$(not in LMFDB)
4.3.i_bh_dm_gy$3$(not in LMFDB)
4.3.l_cf_gy_oo$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
4.3.al_cf_agy_oo$2$(not in LMFDB)
4.3.af_j_a_as$2$(not in LMFDB)
4.3.ab_ad_a_s$2$(not in LMFDB)
4.3.b_ad_a_s$2$(not in LMFDB)
4.3.f_j_a_as$2$(not in LMFDB)
4.3.h_v_bk_cc$2$(not in LMFDB)
4.3.l_cf_gy_oo$2$(not in LMFDB)
4.3.ae_j_as_bk$3$(not in LMFDB)
4.3.ab_ad_a_s$3$(not in LMFDB)
4.3.ab_g_aj_s$3$(not in LMFDB)
4.3.c_d_a_a$3$(not in LMFDB)
4.3.c_m_s_cc$3$(not in LMFDB)
4.3.f_j_a_as$3$(not in LMFDB)
4.3.f_s_bt_dm$3$(not in LMFDB)
4.3.i_bh_dm_gy$3$(not in LMFDB)
4.3.l_cf_gy_oo$3$(not in LMFDB)
4.3.af_p_abe_cc$4$(not in LMFDB)
4.3.ab_d_ag_s$4$(not in LMFDB)
4.3.b_d_g_s$4$(not in LMFDB)
4.3.f_p_be_cc$4$(not in LMFDB)
4.3.ai_bh_adm_gy$6$(not in LMFDB)
4.3.af_s_abt_dm$6$(not in LMFDB)
4.3.ac_d_a_a$6$(not in LMFDB)
4.3.ac_m_as_cc$6$(not in LMFDB)
4.3.b_g_j_s$6$(not in LMFDB)
4.3.e_j_s_bk$6$(not in LMFDB)
4.3.c_d_aj_as$9$(not in LMFDB)
4.3.c_d_j_s$9$(not in LMFDB)
4.3.af_g_p_acc$12$(not in LMFDB)
4.3.ac_a_g_as$12$(not in LMFDB)
4.3.ac_j_am_bk$12$(not in LMFDB)
4.3.ab_ag_d_s$12$(not in LMFDB)
4.3.b_ag_ad_s$12$(not in LMFDB)
4.3.c_a_ag_as$12$(not in LMFDB)
4.3.c_j_m_bk$12$(not in LMFDB)
4.3.f_g_ap_acc$12$(not in LMFDB)
4.3.ac_d_aj_s$18$(not in LMFDB)
4.3.ac_d_j_as$18$(not in LMFDB)
4.3.af_m_ap_s$24$(not in LMFDB)
4.3.ac_g_ag_s$24$(not in LMFDB)
4.3.ab_a_ad_s$24$(not in LMFDB)
4.3.b_a_d_s$24$(not in LMFDB)
4.3.c_g_g_s$24$(not in LMFDB)
4.3.f_m_p_s$24$(not in LMFDB)