Properties

Label 2.107.abm_wc
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:  $( 1 - 20 x + 107 x^{2} )( 1 - 18 x + 107 x^{2} )$
Frobenius angles:  $\pm0.0823304377774$, $\pm0.164078095836$
Angle rank:  $2$ (numerical)
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 7920 127733760 1498731165360 17181743962521600 196717032583030119600 2252195192001181081374720 25785346102879704258090547440 295216379510735944567070392320000 3379932279521031740822863585562375280 38696844627189568061060577746087110348800

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 70 11154 1223410 131078702 14025652550 1500732752706 160578176299730 17181862069197598 1838459214480845830 196715135740789771314

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The isogeny class factors as 1.107.au $\times$ 1.107.as 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_afq$2$(not in LMFDB)
2.107.c_afq$2$(not in LMFDB)
2.107.bm_wc$2$(not in LMFDB)