# Properties

 Label 2.181.abv_biz Base Field $\F_{181}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{181}$ Dimension: $2$ L-polynomial: $1 - 47 x + 909 x^{2} - 8507 x^{3} + 32761 x^{4}$ Frobenius angles: $\pm0.0919956722480$, $\pm0.211005189210$ Angle rank: $2$ (numerical) Number field: 4.0.284445.1 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:

• $y^2=125x^6+84x^5+137x^4+87x^3+139x^2+41x+139$
• $y^2=159x^6+93x^5+160x^4+127x^3+87x^2+125x+50$
• $y^2=130x^6+33x^5+26x^4+93x^3+122x^2+11x+174$
• $y^2=53x^6+173x^5+43x^4+106x^3+122x^2+105x+163$
• $y^2=4x^6+56x^5+125x^4+130x^3+109x^2+107x+32$
• $y^2=10x^6+175x^5+120x^4+38x^3+42x^2+117x+176$
• $y^2=51x^6+32x^5+141x^4+134x^3+99x^2+94x+134$
• $y^2=51x^6+134x^5+99x^4+125x^3+61x^2+33x+155$
• $y^2=122x^6+127x^5+119x^4+157x^3+153x^2+155x+51$
• $y^2=180x^6+124x^5+4x^4+69x^3+32x^2+83x+169$
• $y^2=23x^6+154x^5+25x^4+73x^3+42x+160$
• $y^2=143x^6+173x^5+70x^4+121x^3+124x^2+109x+141$
• $y^2=141x^6+114x^5+162x^4+11x^3+8x^2+9x+175$
• $y^2=97x^6+9x^5+178x^4+94x^3+94x^2+22x+19$
• $y^2=x^6+135x^5+112x^4+94x^3+170x^2+59x+48$
• $y^2=130x^6+x^5+27x^4+162x^3+92x^2+67x+173$
• $y^2=106x^6+157x^5+91x^4+148x^3+54x^2+178x+157$
• $y^2=154x^6+106x^5+180x^4+83x^3+91x^2+177x+154$
• $y^2=96x^6+27x^5+176x^4+121x^3+95x^2+90x+30$
• $y^2=163x^6+154x^5+6x^4+42x^3+168x^2+149x+93$
• $y^2=134x^6+64x^5+33x^4+163x^3+33x^2+84x+30$
• $y^2=18x^6+102x^5+2x^4+129x^3+35x^2+69x+151$
• $y^2=93x^6+166x^5+90x^4+179x^3+2x^2+32x+61$
• $y^2=164x^6+94x^5+103x^4+178x^3+61x^2+132x+104$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 25117 1060565325 35154866511025 1151970369193277925 37738744066132427475712 1236354518735855879699593125 40504199523033080728821168027697 1326958063930020675666160674233852325 43472473122272700693738551503864412684725 1424201691977461542223496191630637775828480000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 135 32371 5928567 1073314531 194265002730 35161838208043 6364291008431715 1151936658077372131 208500535063377589947 37738596846966475988326

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
 The endomorphism algebra of this simple isogeny class is 4.0.284445.1.
All geometric endomorphisms are defined over $\F_{181}$.

## 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 2.181.bv_biz $2$ (not in LMFDB)