# Properties

 Label 2.139.abr_bck 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: $( 1 - 23 x + 139 x^{2} )( 1 - 20 x + 139 x^{2} )$ Frobenius angles: $\pm0.0707251543800$, $\pm0.177693164435$ Angle rank: $2$ (numerical) Jacobians: 12

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 12 curves, and hence is principally polarizable:

• $y^2=127x^6+29x^5+37x^4+119x^3+51x^2+62x+48$
• $y^2=130x^6+81x^5+70x^4+10x^3+44x^2+81x+23$
• $y^2=52x^6+120x^5+113x^4+81x^3+30x^2+134x+44$
• $y^2=114x^6+118x^5+64x^4+64x^3+128x^2+80x+16$
• $y^2=72x^6+101x^5+11x^4+93x^3+50x^2+7x+12$
• $y^2=92x^6+37x^5+20x^4+6x^3+3x^2+138x+84$
• $y^2=108x^6+66x^5+75x^4+93x^3+90x^2+65x+129$
• $y^2=103x^6+28x^5+58x^4+17x^3+61x^2+51x+74$
• $y^2=128x^6+29x^5+96x^4+71x^3+5x^2+100x+3$
• $y^2=27x^6+50x^5+136x^4+135x^3+79x^2+81x+130$
• $y^2=95x^6+87x^5+118x^4+6x^3+26x^2+82x+70$
• $y^2=106x^6+133x^5+60x^4+74x^3+57x^2+85x+14$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 14040 366163200 7206548862240 139353443025638400 2692463915889670408200 52020897823302827495731200 1005095255438196440674349305320 19419444612084003912333544680345600 375203088465633100831063443859455432480 7249298871840739210977088481874386779680000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 97 18949 2683384 373300441 51889070407 7212553404262 1002544413084493 139353667547084401 19370159743384708936 2692452204180515360149

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
 The isogeny class factors as 1.139.ax $\times$ 1.139.au 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.ad_aha $2$ (not in LMFDB) 2.139.d_aha $2$ (not in LMFDB) 2.139.br_bck $2$ (not in LMFDB) 2.139.an_fi $3$ (not in LMFDB) 2.139.ae_abq $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.139.ad_aha $2$ (not in LMFDB) 2.139.d_aha $2$ (not in LMFDB) 2.139.br_bck $2$ (not in LMFDB) 2.139.an_fi $3$ (not in LMFDB) 2.139.ae_abq $3$ (not in LMFDB) 2.139.abk_xa $6$ (not in LMFDB) 2.139.abb_qc $6$ (not in LMFDB) 2.139.e_abq $6$ (not in LMFDB) 2.139.n_fi $6$ (not in LMFDB) 2.139.bb_qc $6$ (not in LMFDB) 2.139.bk_xa $6$ (not in LMFDB)