# Properties

 Label 3.7.ak_cc_agu 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: $( 1 - 4 x + 7 x^{2} )( 1 - 3 x + 7 x^{2} )^{2}$ Frobenius angles: $\pm0.227185525829$, $\pm0.308124534521$, $\pm0.308124534521$ 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 $A(\F_{q^r})$ 100 145200 52561600 15289560000 4796192252500 1615529973657600 556037840198563900 191412267980899680000 65723180397352829915200 22542768937234848538830000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -2 58 436 2642 16978 116716 819838 5759714 40360252 282518218

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
 The isogeny class factors as 1.7.ae $\times$ 1.7.ad 2 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 : $$\Q(\sqrt{-3})$$. 1.7.ad 2 : $\mathrm{M}_{2}($$$\Q(\sqrt{-19})$$$)$
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.ae_m_au $2$ (not in LMFDB) 3.7.ac_g_i $2$ (not in LMFDB) 3.7.c_g_ai $2$ (not in LMFDB) 3.7.e_m_u $2$ (not in LMFDB) 3.7.k_cc_gu $2$ (not in LMFDB) 3.7.ah_bk_aed $3$ (not in LMFDB) 3.7.ab_ad_bi $3$ (not in LMFDB) 3.7.ab_a_bf $3$ (not in LMFDB) 3.7.c_g_bo $3$ (not in LMFDB) 3.7.i_y_ca $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.7.ae_m_au $2$ (not in LMFDB) 3.7.ac_g_i $2$ (not in LMFDB) 3.7.c_g_ai $2$ (not in LMFDB) 3.7.e_m_u $2$ (not in LMFDB) 3.7.k_cc_gu $2$ (not in LMFDB) 3.7.ah_bk_aed $3$ (not in LMFDB) 3.7.ab_ad_bi $3$ (not in LMFDB) 3.7.ab_a_bf $3$ (not in LMFDB) 3.7.c_g_bo $3$ (not in LMFDB) 3.7.i_y_ca $3$ (not in LMFDB) 3.7.ae_c_u $4$ (not in LMFDB) 3.7.e_c_au $4$ (not in LMFDB) 3.7.al_ci_ahr $6$ (not in LMFDB) 3.7.ai_y_aca $6$ (not in LMFDB) 3.7.ah_v_aby $6$ (not in LMFDB) 3.7.af_m_az $6$ (not in LMFDB) 3.7.af_y_acj $6$ (not in LMFDB) 3.7.ae_m_abs $6$ (not in LMFDB) 3.7.ac_ag_bg $6$ (not in LMFDB) 3.7.ac_g_abo $6$ (not in LMFDB) 3.7.ab_m_af $6$ (not in LMFDB) 3.7.b_ad_abi $6$ (not in LMFDB) 3.7.b_a_abf $6$ (not in LMFDB) 3.7.b_m_f $6$ (not in LMFDB) 3.7.c_ag_abg $6$ (not in LMFDB) 3.7.e_m_bs $6$ (not in LMFDB) 3.7.f_m_z $6$ (not in LMFDB) 3.7.f_y_cj $6$ (not in LMFDB) 3.7.h_v_by $6$ (not in LMFDB) 3.7.h_bk_ed $6$ (not in LMFDB) 3.7.l_ci_hr $6$ (not in LMFDB) 3.7.af_c_z $12$ (not in LMFDB) 3.7.ab_c_f $12$ (not in LMFDB) 3.7.b_c_af $12$ (not in LMFDB) 3.7.f_c_az $12$ (not in LMFDB)