# Properties

 Label 3.7.aj_bm_aeh Base Field $\F_{7}$ Dimension $3$ Ordinary Yes $p$-rank $3$ Principally polarizable Yes Contains a Jacobian No

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## Invariants

 Base field: $\F_{7}$ Dimension: $3$ L-polynomial: $( 1 - 5 x + 7 x^{2} )( 1 - 4 x + 11 x^{2} - 28 x^{3} + 49 x^{4} )$ Frobenius angles: $\pm0.106147807505$, $\pm0.158901191781$, $\pm0.538942184569$ 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 $A(\F_{q^r})$ 87 105183 36569232 13454693811 4856713533717 1648938266696448 559622658311689227 191739316707149863275 65755815233310693563184 22542145617400040024253783

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 45 308 2333 17189 119124 825131 5769557 40380284 282510405

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
 The isogeny class factors as 1.7.af $\times$ 2.7.ae_l 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_ac_b $2$ (not in LMFDB) 3.7.b_ac_ab $2$ (not in LMFDB) 3.7.j_bm_eh $2$ (not in LMFDB) 3.7.ad_o_abt $3$ (not in LMFDB) 3.7.a_c_am $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.7.ab_ac_b $2$ (not in LMFDB) 3.7.b_ac_ab $2$ (not in LMFDB) 3.7.j_bm_eh $2$ (not in LMFDB) 3.7.ad_o_abt $3$ (not in LMFDB) 3.7.a_c_am $3$ (not in LMFDB) 3.7.ai_bi_adw $6$ (not in LMFDB) 3.7.af_w_acp $6$ (not in LMFDB) 3.7.a_c_m $6$ (not in LMFDB) 3.7.d_o_bt $6$ (not in LMFDB) 3.7.f_w_cp $6$ (not in LMFDB) 3.7.i_bi_dw $6$ (not in LMFDB)