Properties

Label 2.137.abo_zo
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:  $1 - 40 x + 664 x^{2} - 5480 x^{3} + 18769 x^{4}$
Frobenius angles:  $\pm0.0462922860036$, $\pm0.244475578969$
Angle rank:  $2$ (numerical)
Number field:  4.0.4870400.2
Galois group:  $D_{4}$
Jacobians:  16

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 16 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 13914 347209956 6609900924666 124100072741043216 2329194443295623169114 43716624754577452106212836 820517611717615407044640093306 15400296101032756297602426209894400 289048159646002978862248845573078515994 5425144911139784858947787592159099204068196

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 98 18498 2570594 352281446 48261732658 6611853479202 905824237637074 124097928990786238 17001416396769602018 2329194047535506042178

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The endomorphism algebra of this simple isogeny class is 4.0.4870400.2.
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.bo_zo$2$(not in LMFDB)