Properties

Label 2.107.abl_vh
Base Field $\F_{107}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{107}$
Dimension:  $2$
L-polynomial:  $1 - 37 x + 553 x^{2} - 3959 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.0615358508181$, $\pm0.201040771877$
Angle rank:  $2$ (numerical)
Number field:  4.0.398333.1
Galois group:  $D_{4}$
Jacobians:  7

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains the Jacobians of 7 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8007 128103993 1499326371657 17182164941185149 196716570086744379312 2252193052085463061046601 25785341792303193226682451741 295216373243904014130285016943253 3379932272453669978168176281550580283 38696844621302986076004493509980387205888

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 71 11187 1223897 131081915 14025619576 1500731326791 160578149455627 17181861704462275 1838459210636669297 196715135710865373462

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The endomorphism algebra of this simple isogeny class is 4.0.398333.1.
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.bl_vh$2$(not in LMFDB)