Properties

Label 2.137.abn_yv
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:  $1 - 39 x + 645 x^{2} - 5343 x^{3} + 18769 x^{4}$
Frobenius angles:  $\pm0.0869532210059$, $\pm0.251808753161$
Angle rank:  $2$ (numerical)
Number field:  4.0.15131557.1
Galois group:  $D_{4}$
Jacobians:  10

This isogeny class is simple and geometrically 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 10 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 14033 347976301 6612157193537 124105066066076341 2329204294369226148608 43716644237980610222021437 820517652142331959820438862713 15400296185335458614762380481301093 289048159810467469408359084197790033209 5425144911423704708548399494942279854780416

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 99 18539 2571471 352295619 48261936774 6611856425939 905824282264623 124097929670110243 17001416406443177835 2329194047657402219054

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The endomorphism algebra of this simple isogeny class is 4.0.15131557.1.
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.bn_yv$2$(not in LMFDB)