Properties

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

Learn more about

Invariants

Base field:  $\F_{13^{2}}$
Dimension:  $2$
L-polynomial:  $( 1 - 13 x )^{2}( 1 - 20 x + 169 x^{2} )$
Frobenius angles:  $0$, $0$, $\pm0.220639651288$
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
$A(\F_{q^r})$ 21600 804384000 23287205743200 665413472102400000 19004958441440194428000 542800663678457499391776000 15502932239712970008873815560800 442779261888025523712270923366400000 12646218547962601326904502478412935266400 361188648075114957512618021817280424973600000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 124 28162 4824556 815726878 137858453164 23298080542882 3937376242723516 665416606344634558 112455406909560624604 19004963774385324228802

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13^{2}}$
The isogeny class factors as 1.169.aba $\times$ 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.ag_aha$2$(not in LMFDB)
2.169.g_aha$2$(not in LMFDB)
2.169.bu_bha$2$(not in LMFDB)