Properties

Label 3.7.an_cz_akc
Base Field $\F_{7}$
Dimension $3$
Ordinary Yes
$p$-rank $3$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{7}$
Dimension:  $3$
L-polynomial:  $( 1 - 5 x + 7 x^{2} )( 1 - 4 x + 7 x^{2} )^{2}$
Frobenius angles:  $\pm0.106147807505$, $\pm0.227185525829$, $\pm0.227185525829$
Angle rank:  $1$ (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
$A(\F_{q^r})$ 48 89856 42928704 14821208064 4889951756688 1640360041721856 558709157229483504 191455107206130892800 65691875420472321139392 22538448577696454233249536

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 35 364 2567 17305 118508 823783 5761007 40341028 282464075

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
The isogeny class factors as 1.7.af $\times$ 1.7.ae 2 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 $\overline{\F}_{7}$
The base change of $A$ to $\F_{7^{6}}$ is 1.117649.la 3 and its endomorphism algebra is $\mathrm{M}_{3}($\(\Q(\sqrt{-3}) \)$)$
All geometric endomorphisms are defined over $\F_{7^{6}}$.
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
3.7.af_f_k$2$(not in LMFDB)
3.7.ad_ad_bm$2$(not in LMFDB)
3.7.d_ad_abm$2$(not in LMFDB)
3.7.f_f_ak$2$(not in LMFDB)
3.7.n_cz_kc$2$(not in LMFDB)
3.7.ak_by_age$3$(not in LMFDB)
3.7.ah_bd_ade$3$(not in LMFDB)
3.7.ah_bg_adz$3$(not in LMFDB)
3.7.ae_ae_bs$3$(not in LMFDB)
3.7.ae_f_i$3$(not in LMFDB)
3.7.ae_u_aca$3$(not in LMFDB)
3.7.ab_ae_l$3$(not in LMFDB)
3.7.ab_f_c$3$(not in LMFDB)
3.7.ab_u_an$3$(not in LMFDB)
3.7.c_c_i$3$(not in LMFDB)
3.7.c_o_bg$3$(not in LMFDB)
3.7.f_ae_acd$3$(not in LMFDB)
3.7.f_f_ak$3$(not in LMFDB)
3.7.f_u_cn$3$(not in LMFDB)
3.7.i_bg_do$3$(not in LMFDB)
3.7.l_ce_gx$3$(not in LMFDB)
3.7.o_di_lk$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.7.af_f_k$2$(not in LMFDB)
3.7.ad_ad_bm$2$(not in LMFDB)
3.7.d_ad_abm$2$(not in LMFDB)
3.7.f_f_ak$2$(not in LMFDB)
3.7.n_cz_kc$2$(not in LMFDB)
3.7.ak_by_age$3$(not in LMFDB)
3.7.ah_bd_ade$3$(not in LMFDB)
3.7.ah_bg_adz$3$(not in LMFDB)
3.7.ae_ae_bs$3$(not in LMFDB)
3.7.ae_f_i$3$(not in LMFDB)
3.7.ae_u_aca$3$(not in LMFDB)
3.7.ab_ae_l$3$(not in LMFDB)
3.7.ab_f_c$3$(not in LMFDB)
3.7.ab_u_an$3$(not in LMFDB)
3.7.c_c_i$3$(not in LMFDB)
3.7.c_o_bg$3$(not in LMFDB)
3.7.f_ae_acd$3$(not in LMFDB)
3.7.f_f_ak$3$(not in LMFDB)
3.7.f_u_cn$3$(not in LMFDB)
3.7.i_bg_do$3$(not in LMFDB)
3.7.l_ce_gx$3$(not in LMFDB)
3.7.o_di_lk$3$(not in LMFDB)
3.7.af_j_ak$4$(not in LMFDB)
3.7.f_j_k$4$(not in LMFDB)
3.7.ap_ds_amx$6$(not in LMFDB)
3.7.ao_di_alk$6$(not in LMFDB)
3.7.am_cr_aiy$6$(not in LMFDB)
3.7.al_ce_agx$6$(not in LMFDB)
3.7.aj_bk_adx$6$(not in LMFDB)
3.7.aj_bt_afm$6$(not in LMFDB)
3.7.ai_bg_ado$6$(not in LMFDB)
3.7.ag_g_q$6$(not in LMFDB)
3.7.ag_be_adk$6$(not in LMFDB)
3.7.af_ae_cd$6$(not in LMFDB)
3.7.af_u_acn$6$(not in LMFDB)
3.7.ad_m_abv$6$(not in LMFDB)
3.7.ad_y_abr$6$(not in LMFDB)
3.7.ac_c_ai$6$(not in LMFDB)
3.7.ac_o_abg$6$(not in LMFDB)
3.7.a_a_au$6$(not in LMFDB)
3.7.a_a_u$6$(not in LMFDB)
3.7.b_ae_al$6$(not in LMFDB)
3.7.b_f_ac$6$(not in LMFDB)
3.7.b_u_n$6$(not in LMFDB)
3.7.d_m_bv$6$(not in LMFDB)
3.7.d_y_br$6$(not in LMFDB)
3.7.e_ae_abs$6$(not in LMFDB)
3.7.e_f_ai$6$(not in LMFDB)
3.7.e_u_ca$6$(not in LMFDB)
3.7.g_g_aq$6$(not in LMFDB)
3.7.g_be_dk$6$(not in LMFDB)
3.7.h_bd_de$6$(not in LMFDB)
3.7.h_bg_dz$6$(not in LMFDB)
3.7.j_bk_dx$6$(not in LMFDB)
3.7.j_bt_fm$6$(not in LMFDB)
3.7.k_by_ge$6$(not in LMFDB)
3.7.m_cr_iy$6$(not in LMFDB)
3.7.p_ds_mx$6$(not in LMFDB)
3.7.af_ag_cn$12$(not in LMFDB)
3.7.af_s_acd$12$(not in LMFDB)
3.7.ae_ag_ca$12$(not in LMFDB)
3.7.ae_j_ai$12$(not in LMFDB)
3.7.ae_s_abs$12$(not in LMFDB)
3.7.ab_ag_n$12$(not in LMFDB)
3.7.ab_j_ac$12$(not in LMFDB)
3.7.ab_s_al$12$(not in LMFDB)
3.7.b_ag_an$12$(not in LMFDB)
3.7.b_j_c$12$(not in LMFDB)
3.7.b_s_l$12$(not in LMFDB)
3.7.e_ag_aca$12$(not in LMFDB)
3.7.e_j_i$12$(not in LMFDB)
3.7.e_s_bs$12$(not in LMFDB)
3.7.f_ag_acn$12$(not in LMFDB)
3.7.f_s_cd$12$(not in LMFDB)
3.7.a_a_abl$18$(not in LMFDB)
3.7.a_a_ar$18$(not in LMFDB)
3.7.a_a_r$18$(not in LMFDB)
3.7.a_a_bl$18$(not in LMFDB)