Properties

Label 2.137.abo_zv
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:  $1 - 40 x + 671 x^{2} - 5480 x^{3} + 18769 x^{4}$
Frobenius angles:  $\pm0.121229875658$, $\pm0.215031711367$
Angle rank:  $2$ (numerical)
Number field:  4.0.2336400.6
Galois group:  $D_{4}$
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 13921 347482081 6612065221444 124109271764841481 2329221605166017932561 43716686178972425411016976 820517721523520710227086686849 15400296253518622097407614372710025 289048159792848213052350345584789561476 5425144911181164952596377467828776480822721

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 98 18512 2571434 352307556 48262295458 6611862769238 905824358859154 124097930219540548 17001416405406837338 2329194047553271884272

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The endomorphism algebra of this simple isogeny class is 4.0.2336400.6.
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_zv$2$(not in LMFDB)