Properties

Label 2.137.abo_zy
Base Field $\F_{137}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{137}$
Dimension:  $2$
L-polynomial:  $( 1 - 20 x + 137 x^{2} )^{2}$
Frobenius angles:  $\pm0.173950867407$, $\pm0.173950867407$
Angle rank:  $1$ (numerical)
Jacobians:  13

This isogeny class is not 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 13 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 13924 347598736 6612992837476 124113193119256576 2329232956424663043364 43716710444394416319047056 820517758478545864758950481316 15400296280665879827572452925440000 289048159738315773525188657390537964004 5425144910897440557982268516169229686007696

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 98 18518 2571794 352318686 48262530658 6611866439222 905824399656274 124097930438297278 17001416402199314018 2329194047431459622678

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The isogeny class factors as 1.137.au 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-37}) \)$)$
All geometric endomorphisms are defined over $\F_{137}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.137.a_aew$2$(not in LMFDB)
2.137.bo_zy$2$(not in LMFDB)
2.137.u_kd$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.137.a_aew$2$(not in LMFDB)
2.137.bo_zy$2$(not in LMFDB)
2.137.u_kd$3$(not in LMFDB)
2.137.a_ew$4$(not in LMFDB)
2.137.au_kd$6$(not in LMFDB)