Properties

Label 3.13.aq_eq_auw
Base Field $\F_{13}$
Dimension $3$
Ordinary Yes
$p$-rank $3$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{13}$
Dimension:  $3$
L-polynomial:  $( 1 - 7 x + 13 x^{2} )( 1 - 6 x + 13 x^{2} )( 1 - 3 x + 13 x^{2} )$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.187167041811$, $\pm0.363422825076$
Angle rank:  $3$ (numerical)

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

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
$A(\F_{q^r})$ 616 4398240 10789402624 23377613212800 51150534515943016 112452094830577582080 247116075883767141604168 542851238517134881136140800 1192549190986974855482957436928 2619987533557127401286211408631200

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 154 2236 28658 371038 4826668 62761606 815806562 10604640748 137858065114

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
The isogeny class factors as 1.13.ah $\times$ 1.13.ag $\times$ 1.13.ad and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{13}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
3.13.ak_bq_afe$2$(not in LMFDB)
3.13.ae_a_w$2$(not in LMFDB)
3.13.ac_ag_cw$2$(not in LMFDB)
3.13.c_ag_acw$2$(not in LMFDB)
3.13.e_a_aw$2$(not in LMFDB)
3.13.k_bq_fe$2$(not in LMFDB)
3.13.q_eq_uw$2$(not in LMFDB)
3.13.ah_bn_afq$3$(not in LMFDB)
3.13.ae_m_ao$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.13.ak_bq_afe$2$(not in LMFDB)
3.13.ae_a_w$2$(not in LMFDB)
3.13.ac_ag_cw$2$(not in LMFDB)
3.13.c_ag_acw$2$(not in LMFDB)
3.13.e_a_aw$2$(not in LMFDB)
3.13.k_bq_fe$2$(not in LMFDB)
3.13.q_eq_uw$2$(not in LMFDB)
3.13.ah_bn_afq$3$(not in LMFDB)
3.13.ae_m_ao$3$(not in LMFDB)
3.13.ao_dw_arg$4$(not in LMFDB)
3.13.ai_bi_aeu$4$(not in LMFDB)
3.13.ag_u_acu$4$(not in LMFDB)
3.13.a_c_adg$4$(not in LMFDB)
3.13.a_c_dg$4$(not in LMFDB)
3.13.g_u_cu$4$(not in LMFDB)
3.13.i_bi_eu$4$(not in LMFDB)
3.13.o_dw_rg$4$(not in LMFDB)
3.13.ao_dy_arm$6$(not in LMFDB)
3.13.al_cx_amk$6$(not in LMFDB)
3.13.ai_bk_aeo$6$(not in LMFDB)
3.13.af_bb_adq$6$(not in LMFDB)
3.13.ac_g_bm$6$(not in LMFDB)
3.13.ab_p_ack$6$(not in LMFDB)
3.13.b_p_ck$6$(not in LMFDB)
3.13.c_g_abm$6$(not in LMFDB)
3.13.e_m_o$6$(not in LMFDB)
3.13.f_bb_dq$6$(not in LMFDB)
3.13.h_bn_fq$6$(not in LMFDB)
3.13.i_bk_eo$6$(not in LMFDB)
3.13.l_cx_mk$6$(not in LMFDB)
3.13.o_dy_rm$6$(not in LMFDB)
3.13.am_di_aoi$12$(not in LMFDB)
3.13.aj_cn_ajy$12$(not in LMFDB)
3.13.ag_bg_ads$12$(not in LMFDB)
3.13.af_bl_aec$12$(not in LMFDB)
3.13.ae_w_abs$12$(not in LMFDB)
3.13.ad_bd_acc$12$(not in LMFDB)
3.13.ac_q_i$12$(not in LMFDB)
3.13.ab_z_ac$12$(not in LMFDB)
3.13.b_z_c$12$(not in LMFDB)
3.13.c_q_ai$12$(not in LMFDB)
3.13.d_bd_cc$12$(not in LMFDB)
3.13.e_w_bs$12$(not in LMFDB)
3.13.f_bl_ec$12$(not in LMFDB)
3.13.g_bg_ds$12$(not in LMFDB)
3.13.j_cn_jy$12$(not in LMFDB)
3.13.m_di_oi$12$(not in LMFDB)