# Properties

 Label 3.7.ak_ca_ago 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: $( 1 - 5 x + 7 x^{2} )( 1 - 3 x + 7 x^{2} )( 1 - 2 x + 7 x^{2} )$ Frobenius angles: $\pm0.106147807505$, $\pm0.308124534521$, $\pm0.376624142786$ Angle rank: $3$ (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 $A(\F_{q^r})$ 90 128700 46539360 14131260000 4677800643450 1617462425779200 558824103126708390 191865363956838000000 65755545242320535283360 22542577064915201368717500

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -2 54 394 2450 16558 116856 823954 5773346 40380118 282515814

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
 The isogeny class factors as 1.7.af $\times$ 1.7.ad $\times$ 1.7.ac 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.
 Twist Extension Degree Common base change 3.7.ag_u_acc $2$ (not in LMFDB) 3.7.ae_k_aba $2$ (not in LMFDB) 3.7.a_c_abe $2$ (not in LMFDB) 3.7.a_c_be $2$ (not in LMFDB) 3.7.e_k_ba $2$ (not in LMFDB) 3.7.g_u_cc $2$ (not in LMFDB) 3.7.k_ca_go $2$ (not in LMFDB) 3.7.ae_w_aby $3$ (not in LMFDB) 3.7.ab_h_k $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.7.ag_u_acc $2$ (not in LMFDB) 3.7.ae_k_aba $2$ (not in LMFDB) 3.7.a_c_abe $2$ (not in LMFDB) 3.7.a_c_be $2$ (not in LMFDB) 3.7.e_k_ba $2$ (not in LMFDB) 3.7.g_u_cc $2$ (not in LMFDB) 3.7.k_ca_go $2$ (not in LMFDB) 3.7.ae_w_aby $3$ (not in LMFDB) 3.7.ab_h_k $3$ (not in LMFDB) 3.7.aj_bv_afu $6$ (not in LMFDB) 3.7.ag_bg_adm $6$ (not in LMFDB) 3.7.af_t_abu $6$ (not in LMFDB) 3.7.ad_l_as $6$ (not in LMFDB) 3.7.ac_q_aw $6$ (not in LMFDB) 3.7.a_o_ag $6$ (not in LMFDB) 3.7.a_o_g $6$ (not in LMFDB) 3.7.b_h_ak $6$ (not in LMFDB) 3.7.c_q_w $6$ (not in LMFDB) 3.7.d_l_s $6$ (not in LMFDB) 3.7.e_w_by $6$ (not in LMFDB) 3.7.f_t_bu $6$ (not in LMFDB) 3.7.g_bg_dm $6$ (not in LMFDB) 3.7.j_bv_fu $6$ (not in LMFDB)