Properties

Label 2.107.abk_ur
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:  $( 1 - 19 x + 107 x^{2} )( 1 - 17 x + 107 x^{2} )$
Frobenius angles:  $\pm0.129482033963$, $\pm0.193011390838$
Angle rank:  $2$ (numerical)
Jacobians:  9

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 9 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8099 128571625 1500467778992 17184295182315625 196719921905547219179 2252197631862719466016000 25785347232192236264243084963 295216378710438436416146153615625 3379932276680887518080914521341102768 38696844622791836935477278423506658945625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 72 11228 1224828 131098164 14025858552 1500734378486 160578183332520 17181862022619556 1838459212935995556 196715135718433936268

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The isogeny class factors as 1.107.at $\times$ 1.107.ar 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.ac_aef$2$(not in LMFDB)
2.107.c_aef$2$(not in LMFDB)
2.107.bk_ur$2$(not in LMFDB)