# Properties

 Label 2.181.abu_bib 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: $1 - 46 x + 885 x^{2} - 8326 x^{3} + 32761 x^{4}$ Frobenius angles: $\pm0.105257672036$, $\pm0.223354207626$ Angle rank: $2$ (numerical) Number field: 4.0.530496.5 Galois group: $D_{4}$ Jacobians: 28

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 28 curves, and hence is principally polarizable:

• $y^2=46x^6+13x^5+67x^4+166x^3+158x^2+32x+43$
• $y^2=105x^6+10x^5+6x^4+111x^3+122x^2+68x+159$
• $y^2=19x^6+100x^5+118x^4+156x^3+62x^2+77x+80$
• $y^2=36x^6+90x^5+159x^4+95x^3+174x^2+28x+104$
• $y^2=90x^6+63x^5+79x^3+148x^2+116x+124$
• $y^2=162x^6+62x^5+3x^4+9x^3+117x^2+24x+94$
• $y^2=37x^6+19x^5+75x^4+155x^3+83x^2+130x+24$
• $y^2=156x^6+41x^5+34x^4+172x^3+12x^2+33x+107$
• $y^2=17x^6+118x^5+59x^4+95x^3+96x^2+155x+100$
• $y^2=110x^6+151x^5+178x^4+56x^3+100x^2+85x+45$
• $y^2=153x^6+114x^5+20x^4+32x^3+177x^2+64x+64$
• $y^2=40x^6+170x^5+123x^4+94x^3+126x^2+176x+115$
• $y^2=26x^6+41x^5+70x^4+55x^3+35x^2+33x+72$
• $y^2=172x^6+179x^5+70x^4+75x^3+68x^2+102x+169$
• $y^2=121x^6+28x^5+82x^4+152x^3+52x^2+106x+148$
• $y^2=104x^6+32x^5+17x^4+66x^3+153x^2+131x+118$
• $y^2=75x^6+119x^5+138x^4+138x^3+125x^2+167x+176$
• $y^2=175x^6+114x^5+120x^4+152x^3+171x^2+38x+63$
• $y^2=113x^6+168x^5+x^4+86x^3+22x^2+60x+126$
• $y^2=163x^6+66x^5+2x^4+44x^3+126x^2+15x+172$
• $y^2=177x^6+132x^5+25x^4+176x^3+50x^2+95x+59$
• $y^2=66x^6+11x^5+153x^4+80x^3+99x^2+18x+19$
• $y^2=62x^6+121x^5+102x^4+148x^3+27x^2+24x+168$
• $y^2=77x^6+125x^5+26x^4+139x^3+154x^2+114x+99$
• $y^2=42x^6+70x^5+6x^4+108x^3+128x^2+114x+163$
• $y^2=142x^6+92x^5+168x^4+72x^3+64x^2+15x+40$
• $y^2=74x^6+83x^5+127x^4+27x^3+x^2+96x+111$
• $y^2=68x^6+5x^5+69x^4+74x^3+144x^2+53x+34$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 25275 1062030225 35160742507500 1151985808901714025 37738770825410933806875 1236354539519145417724170000 40504199492544819903352152995475 1326958063873445730099903689877753225 43472473122751460817131066346206023207500 1424201691980628059900160794148363105905930625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 136 32416 5929558 1073328916 194265140476 35161838799118 6364291003641196 1151936658028259236 208500535065673795678 37738596847050382596976

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
 The endomorphism algebra of this simple isogeny class is 4.0.530496.5.
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.bu_bib $2$ (not in LMFDB)