# Properties

 Label 2.137.abo_zp 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: $( 1 - 23 x + 137 x^{2} )( 1 - 17 x + 137 x^{2} )$ Frobenius angles: $\pm0.0596181899068$, $\pm0.241282780251$ Angle rank: $2$ (numerical) Jacobians: 44

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 44 curves, and hence is principally polarizable:

• $y^2=14x^6+67x^5+66x^4+129x^3+66x^2+67x+14$
• $y^2=4x^6+64x^5+99x^4+74x^3+99x^2+64x+4$
• $y^2=120x^6+82x^5+18x^4+130x^3+94x^2+74x+42$
• $y^2=13x^6+10x^5+107x^4+58x^3+99x^2+9x+72$
• $y^2=93x^6+27x^5+6x^4+25x^3+6x^2+27x+93$
• $y^2=111x^6+34x^5+44x^4+81x^3+36x^2+79x+47$
• $y^2=41x^6+34x^5+36x^4+134x^3+50x^2+2x+88$
• $y^2=103x^6+118x^5+28x^4+19x^3+28x^2+118x+103$
• $y^2=128x^6+121x^5+37x^4+53x^3+60x^2+74x+98$
• $y^2=47x^6+12x^5+58x^4+119x^3+123x^2+39x+122$
• $y^2=42x^6+4x^5+55x^4+23x^3+17x^2+121x+37$
• $y^2=41x^6+41x^4+37x^3+69x^2+78x+83$
• $y^2=89x^6+129x^5+75x^4+102x^3+5x^2+10x+126$
• $y^2=125x^6+125x^5+86x^4+67x^3+68x^2+18x+94$
• $y^2=130x^6+24x^5+33x^4+42x^3+33x^2+24x+130$
• $y^2=75x^6+67x^5+91x^4+18x^3+91x^2+67x+75$
• $y^2=71x^6+97x^5+85x^4+130x^3+85x^2+97x+71$
• $y^2=51x^6+111x^5+136x^4+70x^3+35x^2+23x+79$
• $y^2=9x^6+59x^5+99x^4+127x^3+41x^2+19x+23$
• $y^2=61x^6+24x^5+71x^4+24x^3+120x^2+65x+89$
• and 24 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 13915 347248825 6610210097920 124101391104315625 2329198381471590022075 43716633942068978527436800 820517629438799154713045094955 15400296130592931454394879571815625 289048159691398300972526688669196399360 5425144911210837762627629655639280088445625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 98 18500 2570714 352285188 48261814258 6611854868750 905824257200674 124097929228986628 17001416399439692618 2329194047566011402500

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
 The isogeny class factors as 1.137.ax $\times$ 1.137.ar 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.ag_aen $2$ (not in LMFDB) 2.137.g_aen $2$ (not in LMFDB) 2.137.bo_zp $2$ (not in LMFDB)