# Properties

 Label 3.7.aj_bo_aer 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: $( 1 - 5 x + 7 x^{2} )( 1 - 4 x + 13 x^{2} - 28 x^{3} + 49 x^{4} )$ Frobenius angles: $\pm0.106147807505$, $\pm0.204545263622$, $\pm0.514205363720$ 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 $A(\F_{q^r})$ 93 114855 39211776 13626971475 4845127076823 1648826948321280 559282060852288041 191507412525777976875 65722777207740542585088 22541737097470480089861375

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 49 332 2365 17149 119116 824627 5762581 40360004 282505289

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
 The isogeny class factors as 1.7.af $\times$ 2.7.ae_n 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_a_aj $2$ (not in LMFDB) 3.7.b_a_j $2$ (not in LMFDB) 3.7.j_bo_er $2$ (not in LMFDB) 3.7.ad_q_abr $3$ (not in LMFDB) 3.7.a_e_ae $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.7.ab_a_aj $2$ (not in LMFDB) 3.7.b_a_j $2$ (not in LMFDB) 3.7.j_bo_er $2$ (not in LMFDB) 3.7.ad_q_abr $3$ (not in LMFDB) 3.7.a_e_ae $3$ (not in LMFDB) 3.7.ai_bk_aee $6$ (not in LMFDB) 3.7.af_y_acr $6$ (not in LMFDB) 3.7.a_e_e $6$ (not in LMFDB) 3.7.d_q_br $6$ (not in LMFDB) 3.7.f_y_cr $6$ (not in LMFDB) 3.7.i_bk_ee $6$ (not in LMFDB)