# Properties

 Label 2.139.abq_bbm 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: $1 - 42 x + 714 x^{2} - 5838 x^{3} + 19321 x^{4}$ Frobenius angles: $\pm0.0544053773055$, $\pm0.207067484893$ Angle rank: $2$ (numerical) Number field: 4.0.82000.1 Galois group: $D_{4}$ Jacobians: 24

This isogeny class is simple and geometrically 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:

• $y^2=66x^6+105x^5+113x^4+91x^3+14x^2+12x+5$
• $y^2=100x^6+85x^5+37x^4+129x^3+15x^2+39x+85$
• $y^2=53x^6+30x^5+134x^4+52x^3+60x^2+88x+33$
• $y^2=92x^6+20x^5+71x^4+80x^3+35x^2+119x+104$
• $y^2=87x^6+93x^5+82x^4+112x^3+134x^2+8x+15$
• $y^2=34x^6+3x^5+8x^4+75x^3+136x^2+39x+41$
• $y^2=39x^6+133x^5+44x^4+98x^3+39x^2+62x+67$
• $y^2=92x^6+73x^5+23x^4+106x^3+74x^2+9x+12$
• $y^2=59x^6+85x^5+110x^4+109x^3+76x^2+68x+36$
• $y^2=27x^6+96x^5+99x^4+129x^3+21x^2+40x+133$
• $y^2=106x^6+53x^5+117x^4+4x^3+116x^2+32x+4$
• $y^2=48x^6+137x^5+21x^4+104x^3+28x^2+129x+69$
• $y^2=31x^6+95x^5+86x^4+7x^3+75x^2+33x+7$
• $y^2=64x^6+83x^5+x^4+12x^3+82x^2+62x+100$
• $y^2=4x^6+87x^5+27x^4+103x^3+98x^2+46x+27$
• $y^2=23x^6+51x^5+136x^4+20x^3+2x^2+53x+9$
• $y^2=58x^6+94x^5+76x^4+86x^3+99x^2+87x+3$
• $y^2=21x^6+56x^5+37x^4+71x^3+128x^2+39x+60$
• $y^2=64x^6+15x^5+81x^4+70x^3+21x^2+42x+60$
• $y^2=18x^6+52x^5+51x^4+116x^3+22x^2+48x+105$
• $y^2=61x^6+65x^5+30x^4+21x^3+30x^2+112x+12$
• $y^2=27x^6+87x^5+11x^4+41x^3+40x^2+132x+41$
• $y^2=86x^6+53x^5+34x^4+12x^3+131x^2+119x+3$
• $y^2=41x^6+130x^5+85x^4+116x^3+60x^2+107x+43$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 14156 366866896 7208152259996 139354860035226880 2692460178339168050396 52020876983675721120755536 1005095197489215896069157964556 19419444495195652481982874540462080 375203088286393051649675575302582389996 7249298871650953099251016125706315696929616

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 98 18986 2683982 373304238 51888998378 7212550514906 1002544355282582 139353666708295198 19370159734131297938 2692452204110027159306

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
 The endomorphism algebra of this simple isogeny class is 4.0.82000.1.
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.bq_bbm $2$ (not in LMFDB)