# Properties

 Label 3.7.aj_bp_aev 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: $1 - 9 x + 41 x^{2} - 125 x^{3} + 287 x^{4} - 441 x^{5} + 343 x^{6}$ Frobenius angles: $\pm0.152985916969$, $\pm0.192087895429$, $\pm0.502942660276$ Angle rank: $3$ (numerical) Number field: 6.0.3627911.1 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 $A(\F_{q^r})$ 97 120959 41046811 13891052519 4879565729107 1655693270684999 560247160804921792 191525435461048158791 65708266761304067998357 22539159970511717275802039

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 51 347 2411 17269 119607 826048 5763123 40351091 282472991

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
 The endomorphism algebra of this simple isogeny class is 6.0.3627911.1.
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.j_bp_ev $2$ (not in LMFDB)