Properties

Label 2.107.abj_ty
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 yes

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Invariants

Base field:  $\F_{107}$
Dimension:  $2$
L-polynomial:  $( 1 - 19 x + 107 x^{2} )( 1 - 16 x + 107 x^{2} )$
  $1 - 35 x + 518 x^{2} - 3745 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.129482033963$, $\pm0.218559897265$
Angle rank:  $2$ (numerical)
Jacobians:  $8$
Isomorphism classes:  20

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

Newton polygon

This isogeny class is ordinary.

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

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $8188$ $128944624$ $1501075023856$ $17184801285635776$ $196719801719982712468$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $73$ $11261$ $1225324$ $131102025$ $14025849983$ $1500733592822$ $160578169524629$ $17181861874330129$ $1838459212077006388$ $196715135722395359261$

Jacobians and polarizations

This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:

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.aq 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.ad_adm$2$(not in LMFDB)
2.107.d_adm$2$(not in LMFDB)
2.107.bj_ty$2$(not in LMFDB)