# Properties

 Label 3.7.aj_bp_aex 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: $1 - 9 x + 41 x^{2} - 127 x^{3} + 287 x^{4} - 441 x^{5} + 343 x^{6}$ Frobenius angles: $\pm0.0694611744153$, $\pm0.246479041091$, $\pm0.496921726293$ Angle rank: $3$ (numerical) Number field: 6.0.244361927.1 Galois group: $S_4\times C_2$

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 $A(\F_{q^r})$ 95 118655 40094465 13472681975 4765238252225 1636097906252735 557777384517009920 191291127247769841575 65702482696227733419695 22543253749683243072523775

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 51 341 2339 16869 118203 822408 5756067 40347539 282524291

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
 The endomorphism algebra of this simple isogeny class is 6.0.244361927.1.
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_ex $2$ (not in LMFDB)