Properties

Label 2.137.abn_yr
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:  $1 - 39 x + 641 x^{2} - 5343 x^{3} + 18769 x^{4}$
Frobenius angles:  $\pm0.0483327645413$, $\pm0.263061961588$
Angle rank:  $2$ (numerical)
Number field:  4.0.10441053.1
Galois group:  $D_{4}$
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 14029 347820997 6610951564213 124100116808417829 2329190290697469620224 43716613950287720101099573 820517599527917258500636374853 15400296109021200748403115756134277 289048159710559059144356222079827512333 5425144911282655251143292548891903231721472

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 99 18531 2571003 352281571 48261646614 6611851845123 905824224180051 124097929055158339 17001416400566702139 2329194047596845024366

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The endomorphism algebra of this simple isogeny class is 4.0.10441053.1.
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_yr$2$(not in LMFDB)