# 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

## 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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 80 126720 50348480 15419289600 4873102876400 1627897667235840 556775891143160720 191295812255971737600 65687045301605313884480 22538411559872913691641600

 $r$ 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: 1.7.ae 2 : $\mathrm{M}_{2}($$$\Q(\sqrt{-3})$$$)$ 1.7.ad : $$\Q(\sqrt{-19})$$.
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.
 Twist Extension Degree Common 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.
 Twist Extension Degree Common 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)