Properties

Label 2.169.abt_bgg
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:  $( 1 - 25 x + 169 x^{2} )( 1 - 20 x + 169 x^{2} )$
Frobenius angles:  $\pm0.0885687144757$, $\pm0.220639651288$
Angle rank:  $2$ (numerical)
Jacobians:  32

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 32 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 21750 805837500 23294178747000 665439475217400000 19005042530173093293750 542800910748553337462400000 15502932915715641778131850275750 442779263635084729775730687506400000 12646218552264457350883893894582674163000 361188648085260654355450131977349676148437500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 125 28213 4826000 815758753 137859063125 23298091147618 3937376414412125 665416608970146433 112455406947814508000 19004963774919168805573

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13^{2}}$
The isogeny class factors as 1.169.az $\times$ 1.169.au 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.af_agg$2$(not in LMFDB)
2.169.f_agg$2$(not in LMFDB)
2.169.bt_bgg$2$(not in LMFDB)