# Properties

 Label 2.139.abq_bbn 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: $( 1 - 23 x + 139 x^{2} )( 1 - 19 x + 139 x^{2} )$ Frobenius angles: $\pm0.0707251543800$, $\pm0.201746658314$ Angle rank: $2$ (numerical) Jacobians: 32

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 32 curves, and hence is principally polarizable:

• $y^2=26x^6+124x^5+108x^4+96x^3+108x^2+124x+26$
• $y^2=43x^6+18x^5+74x^4+20x^3+3x^2+24x+109$
• $y^2=103x^6+44x^5+129x^4+71x^3+46x^2+42x+126$
• $y^2=22x^6+118x^5+49x^4+60x^3+49x^2+118x+22$
• $y^2=71x^6+90x^5+120x^4+17x^3+58x^2+16x+61$
• $y^2=127x^6+108x^5+59x^4+29x^3+130x^2+79x+123$
• $y^2=99x^6+27x^5+9x^4+127x^3+9x^2+27x+99$
• $y^2=114x^6+114x^5+77x^4+33x^3+77x^2+114x+114$
• $y^2=50x^6+59x^5+120x^4+32x^3+25x^2+8x+8$
• $y^2=17x^6+106x^5+45x^4+91x^3+45x^2+106x+17$
• $y^2=7x^6+60x^5+27x^4+41x^3+27x^2+60x+7$
• $y^2=62x^6+103x^5+6x^4+5x^3+116x^2+115x+71$
• $y^2=123x^6+66x^4+112x^3+60x^2+78x+37$
• $y^2=76x^6+97x^5+3x^4+66x^3+21x^2+95x+40$
• $y^2=86x^6+65x^5+26x^4+79x^3+9x^2+94x+16$
• $y^2=134x^6+42x^5+90x^4+8x^3+90x^2+42x+134$
• $y^2=35x^6+98x^5+5x^4+115x^3+102x^2+28x+94$
• $y^2=122x^6+102x^5+52x^4+122x^3+52x^2+102x+122$
• $y^2=84x^6+54x^5+108x^4+3x^3+108x^2+54x+84$
• $y^2=93x^6+61x^5+80x^4+111x^3+80x^2+61x+93$
• and 12 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 14157 366906969 7208491386096 139356427372718985 2692465343398114418277 52020890491776484612029696 1005095226972862984133803001517 19419444550237390786724254964542665 375203088375214777213507315953290778096 7249298871775310552130533113434718432540329

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 98 18988 2684108 373308436 51889097918 7212552387766 1002544384691402 139353667103273956 19370159738716790612 2692452204156214591228

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
 The isogeny class factors as 1.139.ax $\times$ 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 are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.139.ae_agd $2$ (not in LMFDB) 2.139.e_agd $2$ (not in LMFDB) 2.139.bq_bbn $2$ (not in LMFDB) 2.139.am_fp $3$ (not in LMFDB) 2.139.ad_aba $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.139.ae_agd $2$ (not in LMFDB) 2.139.e_agd $2$ (not in LMFDB) 2.139.bq_bbn $2$ (not in LMFDB) 2.139.am_fp $3$ (not in LMFDB) 2.139.ad_aba $3$ (not in LMFDB) 2.139.abj_wk $6$ (not in LMFDB) 2.139.aba_pv $6$ (not in LMFDB) 2.139.d_aba $6$ (not in LMFDB) 2.139.m_fp $6$ (not in LMFDB) 2.139.ba_pv $6$ (not in LMFDB) 2.139.bj_wk $6$ (not in LMFDB)