# Properties

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

## 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:

• $y^2=70x^6+73x^5+34x^4+60x^3+7x^2+25x+85$
• $y^2=108x^6+29x^5+108x^4+123x^3+108x^2+29x+108$
• $y^2=44x^6+31x^5+99x^4+126x^3+27x^2+74x+23$
• $y^2=25x^6+8x^5+47x^4+63x^3+116x^2+48x+33$
• $y^2=63x^6+98x^5+89x^4+121x^3+55x^2+71x+129$
• $y^2=11x^6+15x^5+101x^4+117x^3+122x^2+109x+92$
• $y^2=51x^6+82x^5+80x^4+111x^3+23x^2+56x+11$
• $y^2=96x^6+132x^5+135x^4+94x^3+135x^2+132x+96$
• $y^2=86x^6+67x^5+81x^4+72x^3+72x^2+47x+27$
• $y^2=89x^6+43x^5+49x^4+36x^3+81x^2+117x+111$
• $y^2=76x^6+51x^5+124x^4+11x^3+116x^2+16x+1$
• $y^2=91x^6+117x^4+117x^2+91$
• $y^2=104x^6+118x^5+61x^4+105x^3+77x^2+130x+7$

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

 $r$ 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.
 Twist Extension Degree Common 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.
 Twist Extension Degree Common 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)