# Properties

 Label 3.7.aj_bn_aem 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: $( 1 - 5 x + 7 x^{2} )( 1 - 4 x + 12 x^{2} - 28 x^{3} + 49 x^{4} )$ Frobenius angles: $\pm0.106147807505$, $\pm0.182041207691$, $\pm0.527071640754$ 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 109980 37878840 13551735600 4856642851950 1649887421757120 559509476998517730 191621020997352960000 65738473828071997222440 22541475295756331716779900

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 47 320 2351 17189 119192 824963 5765999 40369640 282502007

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
 The isogeny class factors as 1.7.af $\times$ 2.7.ae_m 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.ab_ab_ae $2$ (not in LMFDB) 3.7.b_ab_e $2$ (not in LMFDB) 3.7.j_bn_em $2$ (not in LMFDB) 3.7.ad_p_abs $3$ (not in LMFDB) 3.7.a_d_ai $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.7.ab_ab_ae $2$ (not in LMFDB) 3.7.b_ab_e $2$ (not in LMFDB) 3.7.j_bn_em $2$ (not in LMFDB) 3.7.ad_p_abs $3$ (not in LMFDB) 3.7.a_d_ai $3$ (not in LMFDB) 3.7.ai_bj_aea $6$ (not in LMFDB) 3.7.af_x_acq $6$ (not in LMFDB) 3.7.a_d_i $6$ (not in LMFDB) 3.7.d_p_bs $6$ (not in LMFDB) 3.7.f_x_cq $6$ (not in LMFDB) 3.7.i_bj_ea $6$ (not in LMFDB)