# Properties

 Label 2.139.abo_zt 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: $( 1 - 23 x + 139 x^{2} )( 1 - 17 x + 139 x^{2} )$ Frobenius angles: $\pm0.0707251543800$, $\pm0.243700857809$ Angle rank: $2$ (numerical) Jacobians: 20

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 20 curves, and hence is principally polarizable:

• $y^2=27x^6+34x^5+108x^4+3x^3+97x^2+6x+84$
• $y^2=37x^6+113x^5+81x^4+108x^3+137x^2+36x+107$
• $y^2=54x^6+40x^5+43x^3+47x^2+131x+78$
• $y^2=2x^6+33x^5+50x^4+92x^3+101x^2+111x+19$
• $y^2=138x^6+132x^5+52x^4+49x^3+46x^2+x+60$
• $y^2=50x^6+136x^5+43x^4+110x^3+92x^2+77x+102$
• $y^2=113x^6+90x^5+69x^4+43x^3+78x^2+121x+32$
• $y^2=106x^6+92x^5+68x^4+48x^3+102x^2+68x+45$
• $y^2=73x^6+84x^5+7x^4+110x^3+63x^2+59x+39$
• $y^2=132x^6+68x^5+5x^4+39x^3+79x^2+62x+3$
• $y^2=23x^6+93x^5+56x^4+46x^3+125x^2+136x+30$
• $y^2=101x^6+83x^5+61x^4+127x^3+22x^2+13x+115$
• $y^2=46x^6+97x^5+65x^4+60x^3+61x^2+88x+102$
• $y^2=56x^6+133x^5+2x^4+46x^3+18x^2+118x+45$
• $y^2=128x^6+67x^5+41x^4+80x^3+49x^2+121x+123$
• $y^2=103x^6+24x^5+66x^4+3x^3+6x^2+84x+35$
• $y^2=122x^6+35x^5+36x^4+42x^3+71x^2+49x+65$
• $y^2=109x^6+74x^5+115x^4+90x^3+116x^2+62x+132$
• $y^2=66x^6+112x^5+27x^4+135x^3+27x^2+112x+66$
• $y^2=32x^6+113x^5+133x^4+35x^3+32x^2+79x+98$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 14391 368280081 7211474931024 139358953709309529 2692459997933940632151 52020864505831010897592576 1005095171424143328920258194431 19419444483958775435838570013831209 375203088377917546895061526843844022864 7249298871999371988678641492275598205006801

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 100 19060 2685220 373315204 51888994900 7212548784886 1002544329283660 139353666627659524 19370159738856323260 2692452204239432943700

## Decomposition and endomorphism algebra

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

## 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 2.139.ag_aej $2$ (not in LMFDB) 2.139.g_aej $2$ (not in LMFDB) 2.139.bo_zt $2$ (not in LMFDB) 2.139.ak_gd $3$ (not in LMFDB) 2.139.ab_g $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.139.ag_aej $2$ (not in LMFDB) 2.139.g_aej $2$ (not in LMFDB) 2.139.bo_zt $2$ (not in LMFDB) 2.139.ak_gd $3$ (not in LMFDB) 2.139.ab_g $3$ (not in LMFDB) 2.139.abh_ve $6$ (not in LMFDB) 2.139.ay_ph $6$ (not in LMFDB) 2.139.b_g $6$ (not in LMFDB) 2.139.k_gd $6$ (not in LMFDB) 2.139.y_ph $6$ (not in LMFDB) 2.139.bh_ve $6$ (not in LMFDB)