Properties

Label 2.107.abj_tu
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:  $( 1 - 20 x + 107 x^{2} )( 1 - 15 x + 107 x^{2} )$
Frobenius angles:  $\pm0.0823304377774$, $\pm0.241815531636$
Angle rank:  $2$ (numerical)
Jacobians:  24

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 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8184 128848896 1500559020576 17183314024943616 196716856325169708264 2252192084462949092868096 25785340152318845468648047176 295216372600278276830255400960000 3379932274916608318516697882512909344 38696844628148050666422251347134786794496

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 73 11253 1224904 131090681 14025639983 1500730682022 160578139242629 17181861667002673 1838459211976344568 196715135745662210853

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The isogeny class factors as 1.107.au $\times$ 1.107.ap 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.af_adi$2$(not in LMFDB)
2.107.f_adi$2$(not in LMFDB)
2.107.bj_tu$2$(not in LMFDB)