Properties

Label 2.169.abu_bha
Base field $\F_{13^{2}}$
Dimension $2$
$p$-rank $1$
Ordinary no
Supersingular no
Simple no
Geometrically simple no
Primitive yes
Principally polarizable yes
Contains a Jacobian no

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Invariants

Base field:  $\F_{13^{2}}$
Dimension:  $2$
L-polynomial:  $( 1 - 13 x )^{2}( 1 - 20 x + 169 x^{2} )$
  $1 - 46 x + 858 x^{2} - 7774 x^{3} + 28561 x^{4}$
Frobenius angles:  $0$, $0$, $\pm0.220639651288$
Angle rank:  $1$ (numerical)
Jacobians:  $0$

This isogeny class is not simple, primitive, not ordinary, and not supersingular. It is principally polarizable.

Newton polygon

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

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $21600$ $804384000$ $23287205743200$ $665413472102400000$ $19004958441440194428000$

Point counts of the (virtual) curve

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

Jacobians and polarizations

This isogeny class is principally polarizable, but does not contain a Jacobian.

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{13^{2}}$.

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:

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)