# Properties

 Label 3.7.ak_cb_agr 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: $( 1 - 3 x + 7 x^{2} )( 1 - 7 x + 25 x^{2} - 49 x^{3} + 49 x^{4} )$ Frobenius angles: $\pm0.162349854003$, $\pm0.308124534521$, $\pm0.351370772325$ 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 $A(\F_{q^r})$ 95 136895 49521980 14716896975 4746304811600 1620469520571440 558424991759101205 191790410661932100975 65748600161030690773580 22540805470947977630841600

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -2 56 415 2548 16803 117077 823366 5771092 40375855 282493611

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
 The isogeny class factors as 1.7.ad $\times$ 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 is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.7.ae_l_ax $2$ (not in LMFDB) 3.7.e_l_x $2$ (not in LMFDB) 3.7.k_cb_gr $2$ (not in LMFDB)