Properties

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

Learn more about

Invariants

Base field:  $\F_{7}$
Dimension:  $3$
L-polynomial:  $( 1 - 3 x + 7 x^{2} )( 1 - 4 x + 7 x^{2} )^{2}$
Frobenius angles:  $\pm0.227185525829$, $\pm0.227185525829$, $\pm0.308124534521$
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
$A(\F_{q^r})$ 80 126720 50348480 15419289600 4873102876400 1627897667235840 556775891143160720 191295812255971737600 65687045301605313884480 22538411559872913691641600

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 51 420 2663 17247 117612 820929 5756207 40338060 282463611

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
The isogeny class factors as 1.7.ae 2 $\times$ 1.7.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 $\F_{7}$.

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_n_aw$2$(not in LMFDB)
3.7.ad_f_g$2$(not in LMFDB)
3.7.d_f_ag$2$(not in LMFDB)
3.7.f_n_w$2$(not in LMFDB)
3.7.l_cj_hu$2$(not in LMFDB)
3.7.ai_bo_aeu$3$(not in LMFDB)
3.7.af_bc_acv$3$(not in LMFDB)
3.7.ac_ac_bg$3$(not in LMFDB)
3.7.b_e_bd$3$(not in LMFDB)
3.7.h_q_x$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.7.af_n_aw$2$(not in LMFDB)
3.7.ad_f_g$2$(not in LMFDB)
3.7.d_f_ag$2$(not in LMFDB)
3.7.f_n_w$2$(not in LMFDB)
3.7.l_cj_hu$2$(not in LMFDB)
3.7.ai_bo_aeu$3$(not in LMFDB)
3.7.af_bc_acv$3$(not in LMFDB)
3.7.ac_ac_bg$3$(not in LMFDB)
3.7.b_e_bd$3$(not in LMFDB)
3.7.h_q_x$3$(not in LMFDB)
3.7.ad_j_ag$4$(not in LMFDB)
3.7.d_j_g$4$(not in LMFDB)
3.7.an_cy_ajx$6$(not in LMFDB)
3.7.am_cq_aiu$6$(not in LMFDB)
3.7.aj_bs_afl$6$(not in LMFDB)
3.7.ah_q_ax$6$(not in LMFDB)
3.7.ah_bc_adf$6$(not in LMFDB)
3.7.ag_o_ay$6$(not in LMFDB)
3.7.ag_ba_acu$6$(not in LMFDB)
3.7.ae_e_e$6$(not in LMFDB)
3.7.ad_ae_bh$6$(not in LMFDB)
3.7.ad_i_abb$6$(not in LMFDB)
3.7.ad_u_abn$6$(not in LMFDB)
3.7.ac_k_aq$6$(not in LMFDB)
3.7.ab_e_abd$6$(not in LMFDB)
3.7.ab_q_ar$6$(not in LMFDB)
3.7.a_i_am$6$(not in LMFDB)
3.7.a_i_m$6$(not in LMFDB)
3.7.b_q_r$6$(not in LMFDB)
3.7.c_ac_abg$6$(not in LMFDB)
3.7.c_k_q$6$(not in LMFDB)
3.7.d_ae_abh$6$(not in LMFDB)
3.7.d_i_bb$6$(not in LMFDB)
3.7.d_u_bn$6$(not in LMFDB)
3.7.e_e_ae$6$(not in LMFDB)
3.7.f_bc_cv$6$(not in LMFDB)
3.7.g_o_y$6$(not in LMFDB)
3.7.g_ba_cu$6$(not in LMFDB)
3.7.h_bc_df$6$(not in LMFDB)
3.7.i_bo_eu$6$(not in LMFDB)
3.7.j_bs_fl$6$(not in LMFDB)
3.7.m_cq_iu$6$(not in LMFDB)
3.7.n_cy_jx$6$(not in LMFDB)
3.7.ad_ag_bn$12$(not in LMFDB)
3.7.ad_s_abh$12$(not in LMFDB)
3.7.d_ag_abn$12$(not in LMFDB)
3.7.d_s_bh$12$(not in LMFDB)