# Properties

 Label 3.7.am_cp_aip 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: $( 1 - 5 x + 7 x^{2} )( 1 - 7 x + 25 x^{2} - 49 x^{3} + 49 x^{4} )$ Frobenius angles: $\pm0.106147807505$, $\pm0.162349854003$, $\pm0.351370772325$ 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 $A(\F_{q^r})$ 57 97071 42224004 14146059759 4762715284272 1632875028862896 560363983937994531 191950117471752464175 65753434806167474684532 22540842492703355938081536

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -4 40 359 2452 16861 117973 826220 5775892 40378823 282494075

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
 The isogeny class factors as 1.7.af $\times$ 2.7.ah_z 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.ac_ad_bb $2$ (not in LMFDB) 3.7.c_ad_abb $2$ (not in LMFDB) 3.7.m_cp_ip $2$ (not in LMFDB) 3.7.ag_z_acv $3$ (not in LMFDB) 3.7.ad_e_c $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.7.ac_ad_bb $2$ (not in LMFDB) 3.7.c_ad_abb $2$ (not in LMFDB) 3.7.m_cp_ip $2$ (not in LMFDB) 3.7.ag_z_acv $3$ (not in LMFDB) 3.7.ad_e_c $3$ (not in LMFDB) 3.7.al_ci_ahq $6$ (not in LMFDB) 3.7.ai_bn_aet $6$ (not in LMFDB) 3.7.d_e_ac $6$ (not in LMFDB) 3.7.g_z_cv $6$ (not in LMFDB) 3.7.i_bn_et $6$ (not in LMFDB) 3.7.l_ci_hq $6$ (not in LMFDB)