# 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

## 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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 20880 798033600 23262659645760 665349421332960000 19004843119986491360400 542800567622822148812390400 15502932490406956769473418791440 442779263352696825748582128754560000 12646218552262070038872832782173759987520 361188648084197160198237364463377236664440000

 $r$ 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: 1.169.aba : the quaternion algebra over $$\Q$$ ramified at $13$ and $\infty$. 1.169.az : $$\Q(\sqrt{-51})$$.
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.
 Twist Extension Degree Common 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)