# Properties

 Label 3.7.aj_bq_afb 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: $( 1 - 5 x + 7 x^{2} )( 1 - 4 x + 15 x^{2} - 28 x^{3} + 49 x^{4} )$ Frobenius angles: $\pm0.106147807505$, $\pm0.250816204349$, $\pm0.483874642948$ 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 $A(\F_{q^r})$ 99 124839 41955408 13714937379 4788093539889 1641348592595712 558939213215845407 191417022372347246475 65709450332466262269552 22544387121482673630410799

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 53 356 2381 16949 118580 824123 5759861 40351820 282538493

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
 The isogeny class factors as 1.7.af $\times$ 2.7.ae_p 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_c_at $2$ (not in LMFDB) 3.7.b_c_t $2$ (not in LMFDB) 3.7.j_bq_fb $2$ (not in LMFDB) 3.7.ad_s_abp $3$ (not in LMFDB) 3.7.a_g_e $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.7.ab_c_at $2$ (not in LMFDB) 3.7.b_c_t $2$ (not in LMFDB) 3.7.j_bq_fb $2$ (not in LMFDB) 3.7.ad_s_abp $3$ (not in LMFDB) 3.7.a_g_e $3$ (not in LMFDB) 3.7.ai_bm_aem $6$ (not in LMFDB) 3.7.af_ba_act $6$ (not in LMFDB) 3.7.a_g_ae $6$ (not in LMFDB) 3.7.d_s_bp $6$ (not in LMFDB) 3.7.f_ba_ct $6$ (not in LMFDB) 3.7.i_bm_em $6$ (not in LMFDB)