Properties

Label 2.169.abu_bhf
Base Field $\F_{13^{2}}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{13^{2}}$
Dimension:  $2$
L-polynomial:  $( 1 - 25 x + 169 x^{2} )( 1 - 21 x + 169 x^{2} )$
Frobenius angles:  $\pm0.0885687144757$, $\pm0.200716263733$
Angle rank:  $2$ (numerical)
Jacobians:  24

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains the Jacobians of 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 21605 804678225 23290541556560 665433956969861625 19005047856882235388525 542800972688938165079654400 15502933129809347360408818190765 442779264084298243996746535316531625 12646218552689583593035234652664573603920 361188648084198486761338212463730622692330625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 124 28172 4825246 815751988 137859101764 23298093806222 3937376468786836 665416609645232548 112455406951594906414 19004963774863279849052

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13^{2}}$
The isogeny class factors as 1.169.az $\times$ 1.169.av 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 $\F_{13^{2}}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.169.ae_ahf$2$(not in LMFDB)
2.169.e_ahf$2$(not in LMFDB)
2.169.bu_bhf$2$(not in LMFDB)