# Properties

 Label 2.191.abw_bkp Base Field $\F_{191}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{191}$ Dimension: $2$ L-polynomial: $1 - 48 x + 951 x^{2} - 9168 x^{3} + 36481 x^{4}$ Frobenius angles: $\pm0.0856585252156$, $\pm0.218971105078$ Angle rank: $2$ (numerical) Number field: 4.0.13040272.1 Galois group: $D_{4}$ Jacobians: 16

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 16 curves, and hence is principally polarizable:

• $y^2=88x^6+22x^5+34x^4+146x^3+58x^2+46x+45$
• $y^2=187x^6+95x^5+44x^4+26x^3+105x^2+145x+55$
• $y^2=61x^6+189x^5+153x^4+29x^3+130x^2+183x+126$
• $y^2=111x^6+121x^5+39x^4+69x^3+13x^2+99x+55$
• $y^2=151x^6+179x^5+74x^4+69x^3+72x^2+85x+152$
• $y^2=89x^6+124x^5+134x^4+188x^3+64x^2+57x+64$
• $y^2=28x^6+105x^5+54x^4+x^3+57x^2+78x+69$
• $y^2=5x^6+22x^5+47x^4+x^3+33x^2+79x+22$
• $y^2=92x^6+72x^5+47x^4+155x^3+153x^2+140x+103$
• $y^2=6x^6+98x^5+117x^4+176x^3+89x^2+88x+145$
• $y^2=85x^6+27x^5+151x^4+38x^3+102x^2+166x+140$
• $y^2=109x^6+73x^5+81x^4+146x^3+45x^2+94x+189$
• $y^2=107x^6+113x^5+160x^4+26x^3+163x^2+87x+111$
• $y^2=171x^6+98x^5+58x^4+182x^3+90x^2+190x+186$
• $y^2=143x^6+47x^5+171x^4+113x^3+46x^2+60x+114$
• $y^2=64x^6+116x^5+7x^4+122x^3+58x^2+119x+94$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 28217 1316294833 48543204099908 1771241026132892713 64615235944826395314857 2357221975771722891140516368 85993800555309607637244314794313 3137139823941346827281520078088440777 114445997941912288409691746189053389715268 4175104451031945569148965860833601732926905233

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 144 36080 6966720 1330896228 254195640624 48551234577158 9273284257555728 1771197285222884164 338298681550606970688 64615048177915421324240

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
 The endomorphism algebra of this simple isogeny class is 4.0.13040272.1.
All geometric endomorphisms are defined over $\F_{191}$.

## 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 2.191.bw_bkp $2$ (not in LMFDB)