# Properties

 Label 3.7.ak_ca_agn 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: $1 - 10 x + 52 x^{2} - 169 x^{3} + 364 x^{4} - 490 x^{5} + 343 x^{6}$ Frobenius angles: $\pm0.138002645708$, $\pm0.274328089770$, $\pm0.392516251949$ Angle rank: $3$ (numerical) Number field: 6.0.4770787.1 Galois group: $A_4\times C_2$

This isogeny class is simple and geometrically 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 $A(\F_{q^r})$ 91 130039 47095867 14364237979 4744758184621 1628188753462999 559440586548193987 191746078729927173907 65723224633291763731648 22539575190750992919962599

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -2 54 397 2490 16798 117633 824864 5769762 40360276 282478194

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
 The endomorphism algebra of this simple isogeny class is 6.0.4770787.1.
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.k_ca_gn $2$ (not in LMFDB)