Properties

Label 2.169.abz_bma
Base Field $\F_{13^{2}}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{13^{2}}$
Dimension:  $2$
L-polynomial:  $( 1 - 13 x )^{2}( 1 - 25 x + 169 x^{2} )$
Frobenius angles:  $0$, $0$, $\pm0.0885687144757$
Angle rank:  $1$ (numerical)
Jacobians:  0

This isogeny class is not simple.

Newton polygon

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

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
$A(\F_{q^r})$ 20880 798033600 23262659645760 665349421332960000 19004843119986491360400 542800567622822148812390400 15502932490406956769473418791440 442779263352696825748582128754560000 12646218552262070038872832782173759987520 361188648084197160198237364463377236664440000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 119 27937 4819466 815648353 137857616639 23298076419982 3937376306393831 665416608545768833 112455406947793279034 19004963774863210048177

Decomposition and endomorphism algebra

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

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.ab_ama$2$(not in LMFDB)
2.169.b_ama$2$(not in LMFDB)
2.169.bz_bma$2$(not in LMFDB)