# Properties

 Label 2.181.abu_bie 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: $1 - 46 x + 888 x^{2} - 8326 x^{3} + 32761 x^{4}$ Frobenius angles: $\pm0.128869422289$, $\pm0.209863845130$ Angle rank: $2$ (numerical) Number field: 4.0.4394304.1 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:

• $y^2=21x^6+61x^5+150x^4+152x^3+171x^2+63x+21$
• $y^2=179x^6+160x^5+107x^4+154x^3+106x^2+9x+104$
• $y^2=61x^6+166x^5+140x^4+23x^3+121x^2+52x+48$
• $y^2=58x^6+124x^5+123x^4+165x^3+170x^2+152x+15$
• $y^2=75x^6+108x^5+120x^4+11x^3+136x^2+65x+2$
• $y^2=73x^6+92x^5+167x^4+125x^3+142x^2+105x+119$
• $y^2=92x^6+137x^5+20x^4+20x^3+152x^2+89$
• $y^2=43x^6+118x^5+48x^4+144x^3+33x^2+10x+78$
• $y^2=50x^6+93x^5+37x^4+140x^3+78x^2+68x+100$
• $y^2=178x^6+56x^5+45x^4+9x^3+93x^2+17x+70$
• $y^2=98x^6+87x^4+80x^3+10x^2+101x+173$
• $y^2=48x^6+74x^5+85x^4+2x^3+69x^2+129x+174$
• $y^2=55x^6+58x^5+175x^4+152x^3+115x^2+180x+175$
• $y^2=113x^6+3x^5+58x^4+105x^3+135x^2+29x+17$
• $y^2=94x^6+155x^5+76x^4+163x^3+166x^2+171x+155$
• $y^2=138x^6+109x^5+45x^4+118x^3+143x^2+166x+22$
• $y^2=32x^6+88x^5+172x^4+131x^3+97x^2+144x+43$
• $y^2=29x^6+12x^5+136x^4+66x^3+69x^2+42x+29$
• $y^2=131x^6+170x^5+19x^4+139x^3+38x^2+111x+43$
• $y^2=150x^6+174x^5+13x^4+56x^3+13x^2+153x+101$
• $y^2=22x^6+109x^5+81x^4+97x^3+62x^2+73x+84$
• $y^2=167x^6+100x^5+176x^4+18x^3+73x^2+161x+121$
• $y^2=29x^6+43x^5+98x^4+146x^3+177x^2+169x+62$
• $y^2=174x^6+161x^5+158x^4+56x^3+119x^2+65x+50$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 25278 1062232116 35163200751822 1152001645299224016 37738841063867831322798 1236354773107093111210954644 40504200072427524449303773298142 1326958064780810268054416696232612864 43472473122451322928024269368396291994382 1424201691972125116003425143849911453572691476

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 136 32422 5929972 1073343670 194265502036 35161845442342 6364291094756248 1151936658815945374 208500535064234289112 37738596846825070990102

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
 The endomorphism algebra of this simple isogeny class is 4.0.4394304.1.
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.bu_bie $2$ (not in LMFDB)