Properties

Label 2.169.abu_bhb
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:  $1 - 46 x + 859 x^{2} - 7774 x^{3} + 28561 x^{4}$
Frobenius angles:  $\pm0.0365882703553$, $\pm0.217331560748$
Angle rank:  $2$ (numerical)
Number field:  4.0.153152.1
Galois group:  $D_{4}$
Jacobians:  9

This isogeny class is simple and geometrically 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 9 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 21601 804442841 23287872895552 665417575590166313 19004976451350481472641 542800726774432277306860544 15502932426967155683511828369553 442779262378995878954702371336751177 12646218549149401998470216937242184405568 361188648077906113720823565306520339750893081

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 124 28164 4824694 815731908 137858583804 23298083251086 3937376290281628 665416607082473604 112455406920114147142 19004963774532188818564

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13^{2}}$
The endomorphism algebra of this simple isogeny class is 4.0.153152.1.
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.bu_bhb$2$(not in LMFDB)