# Properties

 Label 2.181.abu_bia 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: $1 - 46 x + 884 x^{2} - 8326 x^{3} + 32761 x^{4}$ Frobenius angles: $\pm0.0978554663067$, $\pm0.226927340693$ Angle rank: $2$ (numerical) Number field: 4.0.16097088.1 Galois group: $D_{4}$ Jacobians: 32

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 32 curves, and hence is principally polarizable:

• $y^2=27x^6+107x^5+180x^4+74x^3+79x^2+26x+76$
• $y^2=15x^6+133x^5+98x^4+146x^3+22x^2+20x+65$
• $y^2=20x^6+116x^5+113x^4+98x^3+89x^2+147x+133$
• $y^2=121x^6+26x^5+83x^4+152x^3+87x^2+65x+149$
• $y^2=177x^6+161x^5+55x^4+129x^3+176x^2+122x+145$
• $y^2=155x^6+42x^5+146x^4+3x^3+99x^2+22x+105$
• $y^2=64x^6+91x^5+131x^4+108x^3+86x^2+158x+110$
• $y^2=98x^6+167x^5+110x^4+73x^3+52x^2+151x+65$
• $y^2=17x^6+23x^5+55x^4+66x^3+111x^2+47x+65$
• $y^2=175x^6+38x^5+139x^4+20x^3+110x^2+81x+53$
• $y^2=80x^6+14x^5+120x^4+115x^3+16x^2+102x+150$
• $y^2=98x^6+31x^5+26x^4+5x^3+162x^2+158x+95$
• $y^2=158x^6+118x^5+56x^4+176x^3+110x^2+9x+120$
• $y^2=150x^6+54x^5+60x^4+128x^3+141x^2+8x+134$
• $y^2=120x^6+122x^5+142x^4+16x^3+154x^2+43x+98$
• $y^2=124x^6+29x^5+60x^4+29x^3+105x^2+103x+32$
• $y^2=90x^6+98x^5+61x^4+93x^3+143x^2+65x+132$
• $y^2=159x^6+156x^5+40x^4+123x^3+4x^2+82x+27$
• $y^2=147x^6+151x^5+142x^4+163x^3+9x^2+76x+90$
• $y^2=118x^6+33x^5+24x^4+161x^3+137x^2+173x+164$
• and 12 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 25274 1061962932 35159923103354 1151980521528452688 37738747233877331169434 1236354459725412691355255508 40504199284856291567904093990746 1326958063488344414927514033801704448 43472473122465875888320546487844151609706 1424201691981962717923354555970970289420990932

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 136 32414 5929420 1073323990 194265019036 35161836529790 6364290971007784 1151936657693951518 208500535064304087304 37738596847085748459374

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
 The endomorphism algebra of this simple isogeny class is 4.0.16097088.1.
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_bia $2$ (not in LMFDB)