# Properties

 Label 2.139.abq_bbp 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: $1 - 42 x + 717 x^{2} - 5838 x^{3} + 19321 x^{4}$ Frobenius angles: $\pm0.100495437984$, $\pm0.187984873465$ Angle rank: $2$ (numerical) Number field: 4.0.591424.1 Galois group: $D_{4}$ Jacobians: 7

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 7 curves, and hence is principally polarizable:

• $y^2=123x^6+94x^5+51x^4+104x^3+57x^2+60x+89$
• $y^2=115x^6+98x^5+97x^4+71x^3+77x^2+36x+72$
• $y^2=113x^6+23x^5+10x^4+10x^3+8x^2+76x+122$
• $y^2=63x^6+3x^5+74x^4+54x^3+9x^2+83x+76$
• $y^2=82x^6+60x^5+87x^4+127x^3+90x^2+61x+64$
• $y^2=85x^6+112x^5+x^4+14x^3+40x^2+40x+101$
• $y^2=68x^6+98x^5+x^4+20x^3+108x^2+107x+51$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 14159 366987121 7209169651172 139359557580163561 2692475608143040452599 52020917006679839138506384 1005095283250287402703188970799 19419444649003305800128254302586249 375203088513243417469677524119687781252 7249298871904599518782892076773875344732001

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 98 18992 2684360 373316820 51889295738 7212556063982 1002544440825998 139353667812016804 19370159745842629640 2692452204204233629952

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
 The endomorphism algebra of this simple isogeny class is 4.0.591424.1.
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_bbp $2$ (not in LMFDB)