Properties

Label 3.13.as_fo_azo
Base field $\F_{13}$
Dimension $3$
$p$-rank $3$
Ordinary yes
Supersingular no
Simple no
Geometrically simple no
Primitive yes
Principally polarizable yes
Contains a Jacobian no

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Invariants

Base field:  $\F_{13}$
Dimension:  $3$
L-polynomial:  $( 1 - 4 x + 13 x^{2} )( 1 - 7 x + 13 x^{2} )^{2}$
  $1 - 18 x + 144 x^{2} - 664 x^{3} + 1872 x^{4} - 3042 x^{5} + 2197 x^{6}$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.0772104791556$, $\pm0.312832958189$
Angle rank:  $2$ (numerical)

This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.

Newton polygon

This isogeny class is ordinary.

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

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $490$ $3889620$ $10369999360$ $23181512860800$ $51035082173203450$

Point counts of the (virtual) curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $-4$ $134$ $2150$ $28418$ $370196$ $4821728$ $62739428$ $815772482$ $10604908430$ $137860295414$

Jacobians and polarizations

This isogeny class is principally polarizable, but does not contain a Jacobian.

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{13}$.

Endomorphism algebra over $\F_{13}$
The isogeny class factors as 1.13.ah 2 $\times$ 1.13.ae and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

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_bg_acm$2$(not in LMFDB)
3.13.ae_ak_do$2$(not in LMFDB)
3.13.e_ak_ado$2$(not in LMFDB)
3.13.k_bg_cm$2$(not in LMFDB)
3.13.s_fo_zo$2$(not in LMFDB)
3.13.aj_bt_agw$3$(not in LMFDB)
3.13.ag_m_aq$3$(not in LMFDB)
3.13.a_bb_aq$3$(not in LMFDB)
3.13.d_v_bm$3$(not in LMFDB)
3.13.g_y_ce$3$(not in LMFDB)

Below is a list of all twists of this isogeny class.

TwistExtension degreeCommon base change
3.13.ak_bg_acm$2$(not in LMFDB)
3.13.ae_ak_do$2$(not in LMFDB)
3.13.e_ak_ado$2$(not in LMFDB)
3.13.k_bg_cm$2$(not in LMFDB)
3.13.s_fo_zo$2$(not in LMFDB)
3.13.aj_bt_agw$3$(not in LMFDB)
3.13.ag_m_aq$3$(not in LMFDB)
3.13.a_bb_aq$3$(not in LMFDB)
3.13.d_v_bm$3$(not in LMFDB)
3.13.g_y_ce$3$(not in LMFDB)
3.13.au_gq_abfi$4$(not in LMFDB)
3.13.ai_e_di$4$(not in LMFDB)
3.13.ag_ak_fi$4$(not in LMFDB)
3.13.ag_bk_afi$4$(not in LMFDB)
3.13.ae_bk_ado$4$(not in LMFDB)
3.13.e_bk_do$4$(not in LMFDB)
3.13.g_ak_afi$4$(not in LMFDB)
3.13.g_bk_fi$4$(not in LMFDB)
3.13.i_e_adi$4$(not in LMFDB)
3.13.u_gq_bfi$4$(not in LMFDB)
3.13.aq_es_avk$6$(not in LMFDB)
3.13.ao_ea_arw$6$(not in LMFDB)
3.13.an_dl_ape$6$(not in LMFDB)
3.13.al_cz_amo$6$(not in LMFDB)
3.13.ai_ba_acq$6$(not in LMFDB)
3.13.ai_ch_aiq$6$(not in LMFDB)
3.13.ah_bp_afm$6$(not in LMFDB)
3.13.ag_y_ace$6$(not in LMFDB)
3.13.af_r_acw$6$(not in LMFDB)
3.13.ae_o_ae$6$(not in LMFDB)
3.13.ae_bj_adk$6$(not in LMFDB)
3.13.ad_v_abm$6$(not in LMFDB)
3.13.ac_ae_dk$6$(not in LMFDB)
3.13.ab_f_ade$6$(not in LMFDB)
3.13.ab_r_o$6$(not in LMFDB)
3.13.a_bb_q$6$(not in LMFDB)
3.13.b_f_de$6$(not in LMFDB)
3.13.b_r_ao$6$(not in LMFDB)
3.13.c_ae_adk$6$(not in LMFDB)
3.13.e_o_e$6$(not in LMFDB)
3.13.e_bj_dk$6$(not in LMFDB)
3.13.f_r_cw$6$(not in LMFDB)
3.13.g_m_q$6$(not in LMFDB)
3.13.h_bp_fm$6$(not in LMFDB)
3.13.i_ba_cq$6$(not in LMFDB)
3.13.i_ch_iq$6$(not in LMFDB)
3.13.j_bt_gw$6$(not in LMFDB)
3.13.l_cz_mo$6$(not in LMFDB)
3.13.n_dl_pe$6$(not in LMFDB)
3.13.o_ea_rw$6$(not in LMFDB)
3.13.q_es_vk$6$(not in LMFDB)
3.13.as_fq_abac$12$(not in LMFDB)
3.13.aq_eu_avu$12$(not in LMFDB)
3.13.ap_ed_asg$12$(not in LMFDB)
3.13.an_dn_api$12$(not in LMFDB)
3.13.al_cd_ahu$12$(not in LMFDB)
3.13.ak_cp_aky$12$(not in LMFDB)
3.13.aj_bv_ags$12$(not in LMFDB)
3.13.ai_q_c$12$(not in LMFDB)
3.13.ag_aj_fc$12$(not in LMFDB)
3.13.ag_c_cc$12$(not in LMFDB)
3.13.ag_m_g$12$(not in LMFDB)
3.13.ag_o_ag$12$(not in LMFDB)
3.13.ag_bj_afc$12$(not in LMFDB)
3.13.ae_aj_dk$12$(not in LMFDB)
3.13.ae_ai_ec$12$(not in LMFDB)
3.13.ae_e_bu$12$(not in LMFDB)
3.13.ae_m_e$12$(not in LMFDB)
3.13.ad_ab_g$12$(not in LMFDB)
3.13.ad_l_as$12$(not in LMFDB)
3.13.ac_t_acy$12$(not in LMFDB)
3.13.ab_af_cg$12$(not in LMFDB)
3.13.ab_h_bi$12$(not in LMFDB)
3.13.b_af_acg$12$(not in LMFDB)
3.13.b_h_abi$12$(not in LMFDB)
3.13.c_t_cy$12$(not in LMFDB)
3.13.d_ab_ag$12$(not in LMFDB)
3.13.d_l_s$12$(not in LMFDB)
3.13.e_aj_adk$12$(not in LMFDB)
3.13.e_ai_aec$12$(not in LMFDB)
3.13.e_e_abu$12$(not in LMFDB)
3.13.e_m_ae$12$(not in LMFDB)
3.13.g_aj_afc$12$(not in LMFDB)
3.13.g_c_acc$12$(not in LMFDB)
3.13.g_m_ag$12$(not in LMFDB)
3.13.g_o_g$12$(not in LMFDB)
3.13.g_bj_fc$12$(not in LMFDB)
3.13.i_q_ac$12$(not in LMFDB)
3.13.j_bv_gs$12$(not in LMFDB)
3.13.k_cp_ky$12$(not in LMFDB)
3.13.l_cd_hu$12$(not in LMFDB)
3.13.n_dn_pi$12$(not in LMFDB)
3.13.p_ed_sg$12$(not in LMFDB)
3.13.q_eu_vu$12$(not in LMFDB)
3.13.s_fq_bac$12$(not in LMFDB)