Properties

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

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Invariants

Base field:  $\F_{7}$
Dimension:  $3$
L-polynomial:  $1 - 10 x + 48 x^{2} - 151 x^{3} + 336 x^{4} - 490 x^{5} + 343 x^{6}$
Frobenius angles:  $\pm0.0156081875517$, $\pm0.205965597128$, $\pm0.470301680800$
Angle rank:  $3$ (numerical)
Number field:  6.0.2476099.1
Galois group:  $C_6$

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
$A(\F_{q^r})$ 77 106183 38913413 13242825211 4716236247107 1634371245422839 558358990899492629 191245468376951707411 65659731385027467668288 22535936195083358308721383

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 46 331 2298 16698 118081 823268 5754690 40321276 282432586

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
The endomorphism algebra of this simple isogeny class is 6.0.2476099.1.
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.k_bw_fv$2$(not in LMFDB)