# Properties

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

# Learn more about

## Invariants

 Base field: $\F_{181}$ Dimension: $2$ L-polynomial: $1 - 47 x + 911 x^{2} - 8507 x^{3} + 32761 x^{4}$ Frobenius angles: $\pm0.110478730961$, $\pm0.201428511501$ Angle rank: $2$ (numerical) Number field: 4.0.398333.1 Galois group: $D_{4}$ Jacobians: 21

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 21 curves, and hence is principally polarizable:

• $y^2=54x^6+76x^5+60x^4+99x^3+71x^2+173x+76$
• $y^2=83x^6+43x^5+112x^4+4x^3+24x^2+110x+58$
• $y^2=110x^6+126x^5+86x^4+116x^3+116x^2+127x+128$
• $y^2=108x^6+22x^5+5x^4+73x^3+32x^2+74x+90$
• $y^2=90x^6+68x^5+132x^4+94x^3+43x^2+148x+164$
• $y^2=31x^6+149x^5+16x^4+108x^3+167x^2+40x+114$
• $y^2=110x^6+173x^5+13x^4+72x^3+90x^2+68x+112$
• $y^2=45x^6+170x^5+98x^4+57x^3+61x^2+84x+43$
• $y^2=70x^6+113x^5+99x^4+10x^3+44x^2+149x+132$
• $y^2=97x^5+46x^4+164x^3+120x^2+97x+82$
• $y^2=159x^6+103x^5+88x^4+55x^3+35x^2+27x+22$
• $y^2=17x^6+24x^5+170x^4+167x^3+77x^2+103x+66$
• $y^2=130x^6+107x^5+75x^4+48x^3+50x^2+162x+81$
• $y^2=46x^6+97x^5+136x^4+17x^3+175x^2+46x+2$
• $y^2=57x^6+87x^5+32x^4+101x^3+180x^2+150x+80$
• $y^2=45x^6+144x^5+22x^4+21x^3+40x^2+14x+22$
• $y^2=112x^6+116x^5+179x^4+103x^3+33x^2+85x+21$
• $y^2=19x^6+53x^5+2x^4+175x^3+103x^2+x+152$
• $y^2=38x^6+152x^5+103x^4+117x^3+18x^2+40x+162$
• $y^2=89x^6+157x^5+5x^4+124x^3+127x^2+143x+37$
• $y^2=154x^6+46x^5+123x^4+74x^3+153x^2+169x+125$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 25119 1060700013 35156541071331 1151981523639451413 37738796109746922216144 1236354706123826855248022733 40504200058083389457018434821299 1326958065099398815898081038627924197 43472473123840719694418615864712918812559 1424201691976282450216379446367490346577303808

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 135 32375 5928849 1073324923 194265270630 35161843537343 6364291092502401 1151936659092513139 208500535070898045471 37738596846935232325190

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
 The endomorphism algebra of this simple isogeny class is 4.0.398333.1.
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_bjb $2$ (not in LMFDB)