# Properties

 Label 2.139.abo_zy Base Field $\F_{139}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{139}$ Dimension: $2$ L-polynomial: $( 1 - 22 x + 139 x^{2} )( 1 - 18 x + 139 x^{2} )$ Frobenius angles: $\pm0.117174211439$, $\pm0.223543330897$ Angle rank: $2$ (numerical) Jacobians: 24

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 24 curves, and hence is principally polarizable:

• $y^2=138x^6+7x^5+120x^4+120x^2+7x+138$
• $y^2=32x^6+98x^5+51x^4+74x^3+119x^2+5x+34$
• $y^2=98x^6+26x^5+105x^4+111x^3+128x^2+2x+32$
• $y^2=85x^6+112x^5+83x^4+x^3+83x^2+112x+85$
• $y^2=28x^6+112x^5+73x^4+113x^3+24x^2+131x+45$
• $y^2=36x^6+110x^5+73x^4+134x^3+92x^2+27x+55$
• $y^2=68x^6+31x^5+104x^4+123x^3+90x^2+100x+47$
• $y^2=126x^6+93x^5+118x^4+6x^3+79x+129$
• $y^2=116x^6+51x^5+58x^4+32x^3+58x^2+51x+116$
• $y^2=96x^6+33x^5+120x^4+91x^3+52x^2+15x+120$
• $y^2=116x^6+27x^5+129x^4+111x^3+117x^2+114x+52$
• $y^2=106x^6+96x^5+15x^4+21x^3+78x^2+10x+15$
• $y^2=35x^6+19x^5+30x^4+129x^3+65x^2+15x+24$
• $y^2=43x^6+13x^5+28x^4+22x^3+118x^2+16x+110$
• $y^2=83x^6+17x^5+26x^4+110x^2+23x+4$
• $y^2=17x^6+54x^5+53x^4+77x^3+27x^2+66x+17$
• $y^2=64x^6+3x^5+126x^4+98x^3+49x^2+83x+73$
• $y^2=102x^6+101x^5+23x^4+130x^3+100x^2+68x+34$
• $y^2=93x^6+135x^5+36x^4+26x^3+36x^2+135x+93$
• $y^2=102x^6+100x^5+58x^4+29x^3+58x^2+100x+102$
• $y^2=37x^6+102x^5+108x^4+48x^3+79x^2+32x+91$
• $y^2=58x^6+31x^5+84x^4+55x^3+84x^2+31x+58$
• $y^2=3x^6+74x^5+131x^4+12x^3+49x^2+39x+26$
• $y^2=107x^6+89x^5+x^4+62x^3+110x^2+2x+125$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 14396 368480016 7213089440924 139365886709412864 2692480546039269410876 52020910635863569160821776 1005095251460868698109388050716 19419444585503731375027728846372864 375203088444644310891543437499454555964 7249298871918277367680609351722032861807376

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 100 19070 2685820 373333774 51889390900 7212555180686 1002544409117260 139353667356344734 19370159742301145860 2692452204209313701150

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
 The isogeny class factors as 1.139.aw $\times$ 1.139.as 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 $\F_{139}$.

## 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 2.139.ae_aeo $2$ (not in LMFDB) 2.139.e_aeo $2$ (not in LMFDB) 2.139.bo_zy $2$ (not in LMFDB)