Properties

Label 2.137.abn_zd
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:  $1 - 39 x + 653 x^{2} - 5343 x^{3} + 18769 x^{4}$
Frobenius angles:  $\pm0.157033176591$, $\pm0.212540234294$
Angle rank:  $2$ (numerical)
Number field:  4.0.645525.5
Galois group:  $D_{4}$
Jacobians:  24

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 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 14041 348287005 6614568638329 124114897097925525 2329231398328468877056 43716698585974874719268845 820517727933761423272978579489 15400296231395646385002157172079525 289048159698395390313348046572036159601 5425144910947865131946462850701163699712000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 99 18555 2572407 352323523 48262498374 6611864645715 905824365935847 124097930041270243 17001416399851251819 2329194047453108559150

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The endomorphism algebra of this simple isogeny class is 4.0.645525.5.
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_zd$2$(not in LMFDB)