Properties

Label 4.3.ah_ba_aco_ey
Base Field $\F_{3}$
Dimension $4$
Ordinary Yes
$p$-rank $4$
Principally polarizable Yes
Contains a Jacobian No

Learn more about

Invariants

Base field:  $\F_{3}$
Dimension:  $4$
L-polynomial:  $( 1 - 2 x + 3 x^{2} )( 1 - 5 x + 13 x^{2} - 25 x^{3} + 39 x^{4} - 45 x^{5} + 27 x^{6} )$
Frobenius angles:  $\pm0.0714477711956$, $\pm0.272071776080$, $\pm0.304086723985$, $\pm0.560185743604$
Angle rank:  $4$ (numerical)

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $4$
Slopes:  $[0, 0, 0, 0, 1, 1, 1, 1]$

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
$A(\F_{q^r})$ 10 9300 621490 46500000 3863596550 261827522100 20243733754240 1813169850000000 154314037806166930 12353429416140532500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 13 33 89 267 673 1922 6417 20229 59993

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{3}$
The isogeny class factors as 1.3.ac $\times$ 3.3.af_n_az and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{3}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
4.3.ad_g_ao_bc$2$(not in LMFDB)
4.3.d_g_o_bc$2$(not in LMFDB)
4.3.h_ba_co_ey$2$(not in LMFDB)