Properties

Label 2.107.abl_vj
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:  $1 - 37 x + 555 x^{2} - 3959 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.102828115080$, $\pm0.182443960365$
Angle rank:  $2$ (numerical)
Number field:  4.0.135725.2
Galois group:  $D_{4}$
Jacobians:  4

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 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8009 128152009 1499599225331 17183019791315981 196718479835445595984 2252196425425118632752961 25785346716611920658915722679 295216379250333495317533304210069 3379932278430988133557923606887259509 38696844625658249625020432519362405498624

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 71 11191 1224119 131088435 14025755736 1500733574587 160578180121745 17181862054041939 1838459213887934333 196715135733005324886

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The endomorphism algebra of this simple isogeny class is 4.0.135725.2.
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_vj$2$(not in LMFDB)