# Properties

 Label 2.139.abo_bab 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: $( 1 - 21 x + 139 x^{2} )( 1 - 19 x + 139 x^{2} )$ Frobenius angles: $\pm0.150285916016$, $\pm0.201746658314$ 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:

• $y^2=27x^6+135x^5+24x^4+4x^3+78x^2+62x+82$
• $y^2=96x^6+44x^5+58x^4+115x^3+104x^2+118x+49$
• $y^2=4x^6+51x^5+104x^4+68x^3+19x^2+35x+83$
• $y^2=81x^6+121x^5+121x^4+36x^3+49x^2+106x+117$
• $y^2=18x^6+91x^5+135x^4+74x^3+87x^2+89x+70$
• $y^2=53x^6+40x^5+48x^4+57x^3+126x^2+15x+50$
• $y^2=53x^6+122x^5+26x^4+94x^3+119x^2+36x+53$
• $y^2=21x^6+50x^5+130x^4+46x^3+12x^2+58x+12$
• $y^2=53x^6+135x^5+130x^4+83x^3+10x^2+74x+101$
• $y^2=53x^6+76x^5+130x^4+21x^3+59x^2+88x+135$
• $y^2=118x^6+133x^5+42x^4+18x^3+124x^2+12x+124$
• $y^2=12x^6+32x^5+49x^4+52x^3+24x^2+90x+130$
• $y^2=52x^6+20x^5+89x^4+115x^3+120x^2+4x+64$
• $y^2=9x^6+90x^5+49x^4+2x^3+16x^2+43x+137$
• $y^2=50x^6+67x^5+111x^4+99x^3+115x^2+x+102$
• $y^2=79x^6+94x^5+74x^4+50x^2+128x+79$
• $y^2=28x^6+21x^5+63x^4+79x^3+89x^2+50x+78$
• $y^2=55x^6+97x^5+106x^4+54x^3+5x^2+94x+1$
• $y^2=110x^6+110x^5+100x^4+52x^3+41x^2+134x+130$
• $y^2=27x^6+28x^5+71x^4+124x^3+125x^2+107x+10$
• $y^2=26x^6+84x^5+111x^4+30x^3+48x^2+88x+115$
• $y^2=84x^6+101x^5+109x^4+13x^3+76x^2+2x+39$
• $y^2=15x^6+117x^5+56x^4+120x^3+2x^2+6x+68$
• $y^2=92x^6+77x^5+108x^4+131x^3+103x^2+24x+115$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 14399 368600001 7214058195344 139370028633106425 2692492625858105380079 52020936520562880739604736 1005095290596673647585925220279 19419444612612587097783922618888425 375203088380482050668775137130713868944 7249298871603457166062759364598553684646241

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 100 19076 2686180 373344868 51889623700 7212558769526 1002544448153740 139353667550877508 19370159738988717820 2692452204092386759556

## Decomposition and endomorphism algebra

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

## 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.ac_aer $2$ (not in LMFDB) 2.139.c_aer $2$ (not in LMFDB) 2.139.bo_bab $2$ (not in LMFDB)