Properties

Label 2.107.abj_ty
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:  $( 1 - 19 x + 107 x^{2} )( 1 - 16 x + 107 x^{2} )$
Frobenius angles:  $\pm0.129482033963$, $\pm0.218559897265$
Angle rank:  $2$ (numerical)
Jacobians:  8

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 contains the Jacobians of 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8188 128944624 1501075023856 17184801285635776 196719801719982712468 2252196452791437165296896 25785345014946341644200336772 295216376162549956921150275619584 3379932275101670966780025401572670704 38696844623571108797291852695797838240624

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

Decomposition and endomorphism algebra

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