# Properties

 Label 2.181.abw_bjw 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: $1 - 48 x + 932 x^{2} - 8688 x^{3} + 32761 x^{4}$ Frobenius angles: $\pm0.0587985007366$, $\pm0.204345036706$ Angle rank: $2$ (numerical) Number field: 4.0.3651840.3 Galois group: $D_{4}$ Jacobians: 20

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 20 curves, and hence is principally polarizable:

• $y^2=12x^6+168x^5+5x^4+9x^3+106x^2+48x+69$
• $y^2=84x^6+133x^5+49x^4+77x^3+16x^2+176x+118$
• $y^2=155x^6+176x^5+64x^4+146x^3+84x^2+118x+86$
• $y^2=24x^6+160x^5+126x^4+22x^3+65x^2+124x+22$
• $y^2=174x^6+106x^5+146x^4+86x^3+141x^2+2x+72$
• $y^2=136x^6+96x^5+20x^4+141x^3+55x^2+167x+30$
• $y^2=85x^6+174x^5+137x^4+70x^3+56x^2+46x+12$
• $y^2=109x^6+178x^5+144x^4+44x^3+108x^2+121x+38$
• $y^2=35x^6+38x^5+46x^4+73x^3+121x^2+53x+170$
• $y^2=141x^6+13x^5+71x^4+134x^3+20x^2+63x+146$
• $y^2=73x^6+126x^5+29x^4+95x^3+133x^2+164x+123$
• $y^2=164x^6+129x^5+105x^4+176x^3+179x^2+54x+31$
• $y^2=54x^6+40x^5+11x^4+153x^3+154x^2+67x+69$
• $y^2=53x^6+146x^5+132x^4+164x^3+156x^2+125x+53$
• $y^2=25x^6+132x^5+171x^4+38x^3+130x^2+33x+9$
• $y^2=110x^6+168x^5+42x^4+162x^3+164x^2+144x+118$
• $y^2=36x^6+60x^5+36x^4+114x^3+96x^2+42x+131$
• $y^2=176x^6+85x^5+152x^4+41x^3+143x^2+11x+158$
• $y^2=104x^6+31x^5+167x^4+50x^3+110x^2+29x+44$
• $y^2=95x^6+13x^5+158x^4+110x^3+74x^2+179x+60$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 24958 1058967940 35147317165438 1151943736680090000 37738664441509340762158 1236354301431439325606384260 40504198947853787926218760298638 1326958062392017732815407870691840000 43472473118113649270503952774262224104798 1424201691966530412748623893438633235855458500

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 134 32322 5927294 1073289718 194264592854 35161832027922 6364290918055694 1151936656742226718 208500535043430152294 37738596846676822148802

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
 The endomorphism algebra of this simple isogeny class is 4.0.3651840.3.
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.bw_bjw $2$ (not in LMFDB)