Properties

Label 2.137.abn_yz
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:  $1 - 39 x + 649 x^{2} - 5343 x^{3} + 18769 x^{4}$
Frobenius angles:  $\pm0.119044191820$, $\pm0.237125912106$
Angle rank:  $2$ (numerical)
Number field:  4.0.8123661.1
Galois group:  $D_{4}$
Jacobians:  32

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 32 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 14037 348131637 6613362884781 124109992828914309 2329217996912502116352 43716672448183407480153381 820517694912626742724675389549 15400296225822592744996956616361925 289048159804412417106537380110883661189 5425144911302036045344117404358561002749952

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 99 18547 2571939 352309603 48262220694 6611860692547 905824329481611 124097929996361731 17001416406087027963 2329194047605165839982

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The endomorphism algebra of this simple isogeny class is 4.0.8123661.1.
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_yz$2$(not in LMFDB)