Properties

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

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Invariants

Base field:  $\F_{13^{2}}$
Dimension:  $2$
L-polynomial:  $( 1 - 25 x + 169 x^{2} )( 1 - 19 x + 169 x^{2} )$
Frobenius angles:  $\pm0.0885687144757$, $\pm0.239161554446$
Angle rank:  $2$ (numerical)
Jacobians:  84

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 84 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 21895 806940225 23297237074240 665442179281049625 19005029097392428768975 542800838163925329227366400 15502932727505618878876326332335 442779263392725118306696807596299625 12646218552530437566099693034715838287680 361188648087687213175678648240886685643580625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 126 28252 4826634 815762068 137858965686 23298088032142 3937376366611254 665416608605924068 112455406950179714106 19004963775046849071052

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13^{2}}$
The isogeny class factors as 1.169.az $\times$ 1.169.at 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.ag_afh$2$(not in LMFDB)
2.169.g_afh$2$(not in LMFDB)
2.169.bs_bfh$2$(not in LMFDB)