# Properties

 Label 2.137.abo_zx 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: $( 1 - 21 x + 137 x^{2} )( 1 - 19 x + 137 x^{2} )$ Frobenius angles: $\pm0.145687313345$, $\pm0.198575263152$ Angle rank: $2$ (numerical) Jacobians: 18

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 18 curves, and hence is principally polarizable:

• $y^2=14x^6+80x^5+40x^4+12x^3+40x^2+80x+14$
• $y^2=86x^6+103x^5+97x^4+34x^3+97x^2+103x+86$
• $y^2=x^6+41x^5+71x^4+16x^3+71x^2+41x+1$
• $y^2=91x^6+29x^5+114x^4+84x^3+114x^2+29x+91$
• $y^2=67x^6+133x^5+33x^4+17x^3+33x^2+133x+67$
• $y^2=77x^6+x^5+107x^4+136x^3+107x^2+x+77$
• $y^2=29x^6+92x^5+134x^4+35x^3+134x^2+92x+29$
• $y^2=62x^6+68x^5+46x^4+22x^3+46x^2+68x+62$
• $y^2=79x^6+85x^5+132x^4+20x^3+132x^2+85x+79$
• $y^2=31x^6+62x^5+59x^4+122x^3+59x^2+62x+31$
• $y^2=79x^6+113x^5+38x^4+115x^3+38x^2+113x+79$
• $y^2=129x^6+98x^5+62x^4+43x^3+62x^2+98x+129$
• $y^2=118x^6+120x^5+74x^4+50x^3+74x^2+120x+118$
• $y^2=45x^6+77x^5+47x^4+94x^3+47x^2+77x+45$
• $y^2=134x^6+97x^5+94x^4+110x^3+94x^2+97x+134$
• $y^2=59x^6+54x^5+62x^4+62x^2+54x+59$
• $y^2=84x^6+40x^5+22x^4+18x^3+22x^2+40x+84$
• $y^2=99x^6+52x^5+67x^4+5x^3+67x^2+52x+99$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 13923 347559849 6612683628096 124111887406693641 2329229191974585343443 43716702492970260576915456 820517746829282002985185539747 15400296274118513324662457055480969 289048159764017139059843085536997985344 5425144911010507202635665988474794981872649

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 98 18516 2571674 352314980 48262452658 6611865236622 905824386795874 124097930385537604 17001416403711033098 2329194047480002870836

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
 The isogeny class factors as 1.137.av $\times$ 1.137.at and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.
 Twist Extension Degree Common base change 2.137.ac_aev $2$ (not in LMFDB) 2.137.c_aev $2$ (not in LMFDB) 2.137.bo_zx $2$ (not in LMFDB)