# Properties

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

## 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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 8010 128176020 1499735657160 17183446433546400 196719426927281726550 2252198071607275840950720 25785349031413968346048924710 295216381833408959214636633052800 3379932280425057693904762751959557480 38696844625815717870132616708094930078100

 $r$ 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.
 Twist Extension Degree Common 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)