Properties

Label 2.107.abl_vk
Base field $\F_{107}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple no
Geometrically simple no
Primitive yes
Principally polarizable yes
Contains a Jacobian no

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Invariants

Base field:  $\F_{107}$
Dimension:  $2$
L-polynomial:  $( 1 - 19 x + 107 x^{2} )( 1 - 18 x + 107 x^{2} )$
  $1 - 37 x + 556 x^{2} - 3959 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.129482033963$, $\pm0.164078095836$
Angle rank:  $2$ (numerical)
Jacobians:  $0$
Isomorphism classes:  6

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

Newton polygon

This isogeny class is ordinary.

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

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $8010$ $128176020$ $1499735657160$ $17183446433546400$ $196719426927281726550$

Point counts of the (virtual) curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $71$ $11193$ $1224230$ $131091689$ $14025823261$ $1500734671506$ $160578194537167$ $17181862204379281$ $1838459214972576050$ $196715135733805813593$

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 $\F_{107}$.

Endomorphism algebra over $\F_{107}$
The isogeny class factors as 1.107.at $\times$ 1.107.as 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
2.107.ab_aey$2$(not in LMFDB)
2.107.b_aey$2$(not in LMFDB)
2.107.bl_vk$2$(not in LMFDB)