# Properties

 Label 2.139.abq_bbr 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: $( 1 - 21 x + 139 x^{2} )^{2}$ Frobenius angles: $\pm0.150285916016$, $\pm0.150285916016$ Angle rank: $1$ (numerical) Jacobians: 11

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 11 curves, and hence is principally polarizable:

• $y^2=10x^6+39x^5+27x^4+71x^3+113x^2+66x+55$
• $y^2=88x^6+86x^5+74x^4+31x^3+125x^2+3x+68$
• $y^2=14x^6+33x^5+33x^4+47x^3+33x^2+33x+14$
• $y^2=135x^6+38x^5+14x^4+71x^3+x^2+93x+56$
• $y^2=132x^6+136x^5+33x^4+47x^3+33x^2+136x+132$
• $y^2=128x^6+111x^5+22x^4+77x^3+106x^2+77x+62$
• $y^2=132x^6+81x^5+45x^4+42x^3+45x^2+81x+132$
• $y^2=56x^6+131x^5+110x^4+72x^3+110x^2+131x+56$
• $y^2=23x^6+96x^5+89x^4+44x^3+6x^2+25x+122$
• $y^2=116x^6+5x^5+122x^4+21x^3+122x^2+5x+116$
• $y^2=53x^6+101x^5+127x^4+83x^3+122x^2+45x+135$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 14161 367067281 7209847933456 139362681831003225 2692485785724163187521 52020942853762762779187456 1005095335953008811347115933241 19419444732804523578244747683549225 375203088599376043387029818677352098576 7249298871879943300508288273939015304348241

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 98 18996 2684612 373325188 51889491878 7212559647606 1002544493394962 139353668413373188 19370159750289295388 2692452204195076097556

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
 The isogeny class factors as 1.139.av 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-115})$$$)$
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.a_agh $2$ (not in LMFDB) 2.139.bq_bbr $2$ (not in LMFDB) 2.139.v_lq $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.139.a_agh $2$ (not in LMFDB) 2.139.bq_bbr $2$ (not in LMFDB) 2.139.v_lq $3$ (not in LMFDB) 2.139.a_gh $4$ (not in LMFDB) 2.139.av_lq $6$ (not in LMFDB)