Properties

Label 3.13.au_gq_abfi
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:  $( 1 - 6 x + 13 x^{2} )( 1 - 7 x + 13 x^{2} )^{2}$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.0772104791556$, $\pm0.187167041811$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 392 3457440 10034898944 23181512860800 51232868046172232 112526703776073646080 247115398537287670388264 542828560531927606535692800 1192547229763648456436745832448 2620003957632192333290694379351200

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 114 2076 28418 371634 4829868 62761434 815772482 10604623308 137858929314

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
The isogeny class factors as 1.13.ah 2 $\times$ 1.13.ag 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.ai_e_di$2$(not in LMFDB)
3.13.ag_ak_fi$2$(not in LMFDB)
3.13.g_ak_afi$2$(not in LMFDB)
3.13.i_e_adi$2$(not in LMFDB)
3.13.u_gq_bfi$2$(not in LMFDB)
3.13.al_cd_ahu$3$(not in LMFDB)
3.13.ai_q_c$3$(not in LMFDB)
3.13.ac_t_acy$3$(not in LMFDB)
3.13.b_h_abi$3$(not in LMFDB)
3.13.e_e_abu$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.13.ai_e_di$2$(not in LMFDB)
3.13.ag_ak_fi$2$(not in LMFDB)
3.13.g_ak_afi$2$(not in LMFDB)
3.13.i_e_adi$2$(not in LMFDB)
3.13.u_gq_bfi$2$(not in LMFDB)
3.13.al_cd_ahu$3$(not in LMFDB)
3.13.ai_q_c$3$(not in LMFDB)
3.13.ac_t_acy$3$(not in LMFDB)
3.13.b_h_abi$3$(not in LMFDB)
3.13.e_e_abu$3$(not in LMFDB)
3.13.as_fo_azo$4$(not in LMFDB)
3.13.ak_bg_acm$4$(not in LMFDB)
3.13.ag_bk_afi$4$(not in LMFDB)
3.13.ae_ak_do$4$(not in LMFDB)
3.13.ae_bk_ado$4$(not in LMFDB)
3.13.e_ak_ado$4$(not in LMFDB)
3.13.e_bk_do$4$(not in LMFDB)
3.13.g_bk_fi$4$(not in LMFDB)
3.13.k_bg_cm$4$(not in LMFDB)
3.13.s_fo_zo$4$(not in LMFDB)
3.13.as_fq_abac$6$(not in LMFDB)
3.13.aq_eu_avu$6$(not in LMFDB)
3.13.ap_ed_asg$6$(not in LMFDB)
3.13.an_dn_api$6$(not in LMFDB)
3.13.ak_cp_aky$6$(not in LMFDB)
3.13.aj_bv_ags$6$(not in LMFDB)
3.13.ag_c_cc$6$(not in LMFDB)
3.13.ag_o_ag$6$(not in LMFDB)
3.13.ag_bj_afc$6$(not in LMFDB)
3.13.ae_ai_ec$6$(not in LMFDB)
3.13.ae_e_bu$6$(not in LMFDB)
3.13.ad_ab_g$6$(not in LMFDB)
3.13.ad_l_as$6$(not in LMFDB)
3.13.ab_af_cg$6$(not in LMFDB)
3.13.ab_h_bi$6$(not in LMFDB)
3.13.b_af_acg$6$(not in LMFDB)
3.13.c_t_cy$6$(not in LMFDB)
3.13.d_ab_ag$6$(not in LMFDB)
3.13.d_l_s$6$(not in LMFDB)
3.13.e_ai_aec$6$(not in LMFDB)
3.13.g_c_acc$6$(not in LMFDB)
3.13.g_o_g$6$(not in LMFDB)
3.13.g_bj_fc$6$(not in LMFDB)
3.13.i_q_ac$6$(not in LMFDB)
3.13.j_bv_gs$6$(not in LMFDB)
3.13.k_cp_ky$6$(not in LMFDB)
3.13.l_cd_hu$6$(not in LMFDB)
3.13.n_dn_pi$6$(not in LMFDB)
3.13.p_ed_sg$6$(not in LMFDB)
3.13.q_eu_vu$6$(not in LMFDB)
3.13.s_fq_bac$6$(not in LMFDB)
3.13.aq_es_avk$12$(not in LMFDB)
3.13.ao_ea_arw$12$(not in LMFDB)
3.13.an_dl_ape$12$(not in LMFDB)
3.13.al_cz_amo$12$(not in LMFDB)
3.13.aj_bt_agw$12$(not in LMFDB)
3.13.ai_ba_acq$12$(not in LMFDB)
3.13.ai_ch_aiq$12$(not in LMFDB)
3.13.ah_bp_afm$12$(not in LMFDB)
3.13.ag_aj_fc$12$(not in LMFDB)
3.13.ag_m_aq$12$(not in LMFDB)
3.13.ag_m_g$12$(not in LMFDB)
3.13.ag_y_ace$12$(not in LMFDB)
3.13.af_r_acw$12$(not in LMFDB)
3.13.ae_aj_dk$12$(not in LMFDB)
3.13.ae_m_e$12$(not in LMFDB)
3.13.ae_o_ae$12$(not in LMFDB)
3.13.ae_bj_adk$12$(not in LMFDB)
3.13.ad_v_abm$12$(not in LMFDB)
3.13.ac_ae_dk$12$(not in LMFDB)
3.13.ab_f_ade$12$(not in LMFDB)
3.13.ab_r_o$12$(not in LMFDB)
3.13.a_bb_aq$12$(not in LMFDB)
3.13.a_bb_q$12$(not in LMFDB)
3.13.b_f_de$12$(not in LMFDB)
3.13.b_r_ao$12$(not in LMFDB)
3.13.c_ae_adk$12$(not in LMFDB)
3.13.d_v_bm$12$(not in LMFDB)
3.13.e_aj_adk$12$(not in LMFDB)
3.13.e_m_ae$12$(not in LMFDB)
3.13.e_o_e$12$(not in LMFDB)
3.13.e_bj_dk$12$(not in LMFDB)
3.13.f_r_cw$12$(not in LMFDB)
3.13.g_aj_afc$12$(not in LMFDB)
3.13.g_m_ag$12$(not in LMFDB)
3.13.g_m_q$12$(not in LMFDB)
3.13.g_y_ce$12$(not in LMFDB)
3.13.h_bp_fm$12$(not in LMFDB)
3.13.i_ba_cq$12$(not in LMFDB)
3.13.i_ch_iq$12$(not in LMFDB)
3.13.j_bt_gw$12$(not in LMFDB)
3.13.l_cz_mo$12$(not in LMFDB)
3.13.n_dl_pe$12$(not in LMFDB)
3.13.o_ea_rw$12$(not in LMFDB)
3.13.q_es_vk$12$(not in LMFDB)