Properties

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

Learn more about

Invariants

Base field:  $\F_{13}$
Dimension:  $3$
L-polynomial:  $( 1 - 7 x + 13 x^{2} )( 1 - 5 x + 13 x^{2} )( 1 - 4 x + 13 x^{2} )$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.256122854178$, $\pm0.312832958189$
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
$A(\F_{q^r})$ 630 4524660 11052236160 23612933635200 51200489634024150 112337097044228259840 246971216439371889206910 542777263568205236101440000 1192552670567179325263778029440 2620021970752207141908792554997300

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 158 2290 28946 371398 4821728 62724814 815695394 10604671690 137859877118

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
The isogeny class factors as 1.13.ah $\times$ 1.13.af $\times$ 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:
Endomorphism algebra over $\overline{\F}_{13}$
The base change of $A$ to $\F_{13^{6}}$ is 1.4826809.agao $\times$ 1.4826809.atm 2 . The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{13^{6}}$.
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
3.13.ai_ba_acq$2$(not in LMFDB)
3.13.ag_m_aq$2$(not in LMFDB)
3.13.ac_ae_dk$2$(not in LMFDB)
3.13.c_ae_adk$2$(not in LMFDB)
3.13.g_m_q$2$(not in LMFDB)
3.13.i_ba_cq$2$(not in LMFDB)
3.13.q_es_vk$2$(not in LMFDB)
3.13.an_dl_ape$3$(not in LMFDB)
3.13.ah_bp_afm$3$(not in LMFDB)
3.13.ae_ak_do$3$(not in LMFDB)
3.13.ae_o_ae$3$(not in LMFDB)
3.13.ae_bj_adk$3$(not in LMFDB)
3.13.ab_r_o$3$(not in LMFDB)
3.13.f_r_cw$3$(not in LMFDB)
3.13.i_ba_cq$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.13.ai_ba_acq$2$(not in LMFDB)
3.13.ag_m_aq$2$(not in LMFDB)
3.13.ac_ae_dk$2$(not in LMFDB)
3.13.c_ae_adk$2$(not in LMFDB)
3.13.g_m_q$2$(not in LMFDB)
3.13.i_ba_cq$2$(not in LMFDB)
3.13.q_es_vk$2$(not in LMFDB)
3.13.an_dl_ape$3$(not in LMFDB)
3.13.ah_bp_afm$3$(not in LMFDB)
3.13.ae_ak_do$3$(not in LMFDB)
3.13.ae_o_ae$3$(not in LMFDB)
3.13.ae_bj_adk$3$(not in LMFDB)
3.13.ab_r_o$3$(not in LMFDB)
3.13.f_r_cw$3$(not in LMFDB)
3.13.i_ba_cq$3$(not in LMFDB)
3.13.as_fq_abac$4$(not in LMFDB)
3.13.ai_q_c$4$(not in LMFDB)
3.13.ag_c_cc$4$(not in LMFDB)
3.13.ae_ai_ec$4$(not in LMFDB)
3.13.e_ai_aec$4$(not in LMFDB)
3.13.g_c_acc$4$(not in LMFDB)
3.13.i_q_ac$4$(not in LMFDB)
3.13.s_fq_bac$4$(not in LMFDB)
3.13.as_fo_azo$6$(not in LMFDB)
3.13.ao_ea_arw$6$(not in LMFDB)
3.13.al_cz_amo$6$(not in LMFDB)
3.13.ak_bg_acm$6$(not in LMFDB)
3.13.aj_bt_agw$6$(not in LMFDB)
3.13.ai_ch_aiq$6$(not in LMFDB)
3.13.ag_y_ace$6$(not in LMFDB)
3.13.af_r_acw$6$(not in LMFDB)
3.13.ad_v_abm$6$(not in LMFDB)
3.13.ab_f_ade$6$(not in LMFDB)
3.13.a_bb_aq$6$(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.d_v_bm$6$(not in LMFDB)
3.13.e_ak_ado$6$(not in LMFDB)
3.13.e_o_e$6$(not in LMFDB)
3.13.e_bj_dk$6$(not in LMFDB)
3.13.g_y_ce$6$(not in LMFDB)
3.13.h_bp_fm$6$(not in LMFDB)
3.13.i_ch_iq$6$(not in LMFDB)
3.13.j_bt_gw$6$(not in LMFDB)
3.13.k_bg_cm$6$(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.s_fo_zo$6$(not in LMFDB)
3.13.au_gq_abfi$12$(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_e_di$12$(not in LMFDB)
3.13.ag_ak_fi$12$(not in LMFDB)
3.13.ag_aj_fc$12$(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.ag_bk_afi$12$(not in LMFDB)
3.13.ae_aj_dk$12$(not in LMFDB)
3.13.ae_e_bu$12$(not in LMFDB)
3.13.ae_m_e$12$(not in LMFDB)
3.13.ae_bk_ado$12$(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_e_abu$12$(not in LMFDB)
3.13.e_m_ae$12$(not in LMFDB)
3.13.e_bk_do$12$(not in LMFDB)
3.13.g_ak_afi$12$(not in LMFDB)
3.13.g_aj_afc$12$(not in LMFDB)
3.13.g_m_ag$12$(not in LMFDB)
3.13.g_o_g$12$(not in LMFDB)
3.13.g_bj_fc$12$(not in LMFDB)
3.13.g_bk_fi$12$(not in LMFDB)
3.13.i_e_adi$12$(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.u_gq_bfi$12$(not in LMFDB)