# Properties

 Label 2.181.abv_bjd 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: $1 - 47 x + 913 x^{2} - 8507 x^{3} + 32761 x^{4}$ Frobenius angles: $\pm0.132251908937$, $\pm0.187299602773$ Angle rank: $2$ (numerical) Number field: 4.0.657725.1 Galois group: $D_{4}$ Jacobians: 13

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 13 curves, and hence is principally polarizable:

• $y^2=153x^6+28x^5+123x^4+122x^3+166x^2+136x+123$
• $y^2=17x^6+180x^5+42x^4+162x^3+41x^2+157x+18$
• $y^2=83x^6+171x^5+11x^4+103x^3+154x^2+96x+22$
• $y^2=113x^6+172x^5+120x^4+115x^3+8x^2+122x+74$
• $y^2=107x^6+62x^5+171x^4+162x^3+15x^2+84x+40$
• $y^2=134x^6+148x^5+100x^4+164x^3+152x^2+38x+137$
• $y^2=162x^6+78x^5+148x^4+4x^3+133x^2+80x+29$
• $y^2=36x^6+82x^5+91x^4+87x^3+79x^2+42x+93$
• $y^2=149x^5+25x^3+135x^2+111x+54$
• $y^2=40x^6+75x^5+2x^4+78x^3+161x^2+154x+22$
• $y^2=167x^6+23x^5+86x^4+42x^3+125x^2+177x+98$
• $y^2=42x^6+129x^5+137x^4+13x^3+173x^2+9x+88$
• $y^2=92x^6+55x^5+104x^4+25x^3+35x^2+175x+49$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 25121 1060834709 35158215653501 1151992660939088309 37738847788163620114176 1236354889456945618976835725 40504200561876683682439253479781 1326958066081782287175268691651760389 43472473124491079096512385428025539779041 1424201691971302584625386989687300753842089984

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 135 32379 5929131 1073335299 194265536650 35161848751323 6364291171661775 1151936659945323459 208500535074017267211 37738596846803275495654

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
 The endomorphism algebra of this simple isogeny class is 4.0.657725.1.
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.bv_bjd $2$ (not in LMFDB)