Properties

Label 2.137.abo_zp
Base Field $\F_{137}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{137}$
Dimension:  $2$
L-polynomial:  $( 1 - 23 x + 137 x^{2} )( 1 - 17 x + 137 x^{2} )$
Frobenius angles:  $\pm0.0596181899068$, $\pm0.241282780251$
Angle rank:  $2$ (numerical)
Jacobians:  44

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 44 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 13915 347248825 6610210097920 124101391104315625 2329198381471590022075 43716633942068978527436800 820517629438799154713045094955 15400296130592931454394879571815625 289048159691398300972526688669196399360 5425144911210837762627629655639280088445625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 98 18500 2570714 352285188 48261814258 6611854868750 905824257200674 124097929228986628 17001416399439692618 2329194047566011402500

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The isogeny class factors as 1.137.ax $\times$ 1.137.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 $\F_{137}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.137.ag_aen$2$(not in LMFDB)
2.137.g_aen$2$(not in LMFDB)
2.137.bo_zp$2$(not in LMFDB)