Properties

Label 2.107.abl_vk
Base Field $\F_{107}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{107}$
Dimension:  $2$
L-polynomial:  $( 1 - 19 x + 107 x^{2} )( 1 - 18 x + 107 x^{2} )$
Frobenius angles:  $\pm0.129482033963$, $\pm0.164078095836$
Angle rank:  $2$ (numerical)
Jacobians:  0

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

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

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
$A(\F_{q^r})$ 8010 128176020 1499735657160 17183446433546400 196719426927281726550 2252198071607275840950720 25785349031413968346048924710 295216381833408959214636633052800 3379932280425057693904762751959557480 38696844625815717870132616708094930078100

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

Decomposition and endomorphism algebra

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:
All geometric endomorphisms are defined over $\F_{107}$.

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)