# Properties

 Label 3.7.al_ch_ahn 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: $1 - 11 x + 59 x^{2} - 195 x^{3} + 413 x^{4} - 539 x^{5} + 343 x^{6}$ Frobenius angles: $\pm0.0413211978612$, $\pm0.265511145545$, $\pm0.363643463851$ Angle rank: $3$ (numerical) Number field: 6.0.400967.1 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 $A(\F_{q^r})$ 71 110831 43933877 13983436439 4666007907401 1611031149891527 556855969625947328 191505738801887923847 65710774036055835559223 22538759336355737710643471

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -3 47 375 2427 16517 116387 821048 5762531 40352631 282467967

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
 The endomorphism algebra of this simple isogeny class is 6.0.400967.1.
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.l_ch_hn $2$ (not in LMFDB)