# Properties

 Label 2.181.abu_bih 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: $( 1 - 23 x + 181 x^{2} )^{2}$ Frobenius angles: $\pm0.173686936480$, $\pm0.173686936480$ Angle rank: $1$ (numerical) Jacobians: 40

This isogeny class is not 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 40 curves, and hence is principally polarizable:

• $y^2=x^6+14x^3+29$
• $y^2=65x^6+76x^5+110x^4+90x^3+127x^2+118x+73$
• $y^2=93x^6+126x^5+129x^4+95x^3+93x^2+50x+74$
• $y^2=125x^6+28x^5+109x^4+111x^3+116x^2+23x+180$
• $y^2=32x^6+23x^5+146x^4+127x^3+132x^2+53x+5$
• $y^2=24x^6+76x^5+30x^4+134x^3+123x^2+54x+28$
• $y^2=77x^6+86x^5+19x^4+113x^3+24x^2+104x+8$
• $y^2=176x^6+131x^5+12x^4+126x^3+94x^2+19x+36$
• $y^2=168x^6+127x^5+116x^4+52x^3+75x^2+146x+158$
• $y^2=40x^6+127x^5+63x^4+155x^3+134x^2+122x+89$
• $y^2=146x^6+59x^5+18x^4+145x^3+148x^2+113x+69$
• $y^2=171x^6+73x^5+133x^4+32x^3+7x^2+61x+159$
• $y^2=30x^6+31x^5+125x^4+145x^3+129x^2+120x+107$
• $y^2=100x^6+160x^5+177x^4+71x^3+126x^2+23x+11$
• $y^2=31x^6+164x^5+151x^4+62x^3+125x^2+81x+90$
• $y^2=85x^6+14x^5+7x^4+85x^3+174x^2+14x+96$
• $y^2=x^6+x^3+132$
• $y^2=131x^6+25x^5+140x^4+79x^3+27x^2+58x+133$
• $y^2=68x^6+9x^5+69x^4+121x^3+2x^2+129x+30$
• $y^2=173x^6+131x^5+66x^4+99x^3+77x^2+123x+175$
• and 20 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 25281 1062434025 35165659044096 1152017443113770025 37738910498109592648041 1236354998014026605269094400 40504200587794120866520568758641 1326958065320149748922401858967398025 43472473120455939405124729965125417431296 1424201691957191884541184602876158683016265625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 136 32428 5930386 1073358388 194265859456 35161851838678 6364291175734096 1151936659284147748 208500535054664128906 37738596846429369169948

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
 The isogeny class factors as 1.181.ax 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-195})$$$)$
All geometric endomorphisms are defined over $\F_{181}$.

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.181.a_agl $2$ (not in LMFDB) 2.181.bu_bih $2$ (not in LMFDB) 2.181.x_nk $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.181.a_agl $2$ (not in LMFDB) 2.181.bu_bih $2$ (not in LMFDB) 2.181.x_nk $3$ (not in LMFDB) 2.181.a_gl $4$ (not in LMFDB) 2.181.ax_nk $6$ (not in LMFDB)