# Properties

 Label 2.181.abz_bmx Base Field $\F_{181}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

# Learn more about

## Invariants

 Base field: $\F_{181}$ Dimension: $2$ L-polynomial: $1 - 51 x + 1011 x^{2} - 9231 x^{3} + 32761 x^{4}$ Frobenius angles: $\pm0.0467121644153$, $\pm0.139008714891$ Angle rank: $2$ (numerical) Number field: 4.0.50125.1 Galois group: $D_{4}$ Jacobians: 4

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 4 curves, and hence is principally polarizable:

• $y^2=17x^6+4x^5+101x^4+9x^3+130x^2+151x+166$
• $y^2=161x^6+25x^5+166x^4+14x^3+129x^2+151x+22$
• $y^2=135x^6+51x^5+156x^4+48x^3+40x^2+75x+64$
• $y^2=61x^6+88x^5+146x^4+56x^3+14x^2+152x+146$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 24491 1054460005 35128277447231 1151890423380452005 37738568154960421158416 1236354267375807197377086805 40504199492711841015405998056151 1326958065002999300604090776449398405 43472473125583976609943105146194167462131 1424201691980506209640360423146178676020000000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 131 32183 5924081 1073240043 194264097206 35161831059383 6364291003667441 1151936659008828403 208500535079258968451 37738596847047153800198

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
 The endomorphism algebra of this simple isogeny class is 4.0.50125.1.
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.bz_bmx $2$ (not in LMFDB)