Properties

Label 2.169.aby_bla
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:  $( 1 - 13 x )^{2}( 1 - 24 x + 169 x^{2} )$
Frobenius angles:  $0$, $0$, $\pm0.125665916378$
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
$A(\F_{q^r})$ 21024 799416576 23268899852064 665370404536320000 19004901566295727075104 542800706483172827618724096 15502932767769163053791360922144 442779263776688659925320126955520000 12646218552531220140261393123616485425184 361188648082918367988225092855510083772610816

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 120 27986 4820760 815674078 137858040600 23298082380146 3937376376837240 665416609182951358 112455406950186673080 19004963774795922773906

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13^{2}}$
The isogeny class factors as 1.169.aba $\times$ 1.169.ay 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 are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.169.ac_ala$2$(not in LMFDB)
2.169.c_ala$2$(not in LMFDB)
2.169.by_bla$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.169.ac_ala$2$(not in LMFDB)
2.169.c_ala$2$(not in LMFDB)
2.169.by_bla$2$(not in LMFDB)
2.169.abk_xa$4$(not in LMFDB)
2.169.aq_da$4$(not in LMFDB)
2.169.q_da$4$(not in LMFDB)
2.169.bk_xa$4$(not in LMFDB)