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

Learn more about

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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 71 110831 43933877 13983436439 4666007907401 1611031149891527 556855969625947328 191505738801887923847 65710774036055835559223 22538759336355737710643471

Point counts of the (virtual) curve

$r$ 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.
TwistExtension DegreeCommon base change
3.7.l_ch_hn$2$(not in LMFDB)