# Properties

 Label 3.7.aj_bm_aei Base Field $\F_{7}$ Dimension $3$ Ordinary No $p$-rank $2$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{7}$ Dimension: $3$ L-polynomial: $1 - 9 x + 38 x^{2} - 112 x^{3} + 266 x^{4} - 441 x^{5} + 343 x^{6}$ Frobenius angles: $\pm0.0283467889665$, $\pm0.193732293337$, $\pm0.536888824784$ Angle rank: $3$ (numerical) Number field: 6.0.30088184.1 Galois group: $S_4\times C_2$

This isogeny class is simple and geometrically simple.

## Newton polygon

 $p$-rank: $2$ Slopes: $[0, 0, 1/2, 1/2, 1, 1]$

## 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 $A(\F_{q^r})$ 86 104060 36096350 13240594400 4794339367136 1635819081825500 557193261508696262 191339982259009865600 65701512455397896151950 22536096965623129594956800

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 45 305 2297 16974 118185 821547 5757537 40346945 282434600

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
 The endomorphism algebra of this simple isogeny class is 6.0.30088184.1.
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_bm_ei $2$ (not in LMFDB)