# Properties

 Label 1.181.aba Base Field $\F_{181}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{181}$ Dimension: $1$ L-polynomial: $1 - 26 x + 181 x^{2}$ Frobenius angles: $\pm0.0828936782352$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-3})$$ Galois group: $C_2$ Jacobians: 4

This isogeny class is simple and geometrically simple.

## Newton polygon

This isogeny class is ordinary.

 $p$-rank: $1$ Slopes: $[0, 1]$

## Point counts

This isogeny class contains the Jacobians of 4 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 156 32448 5926284 1073250048 194264010876 35161828228800 6364290967005036 1151936658876177408 208500535086218801244 37738596847289464820928

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 156 32448 5926284 1073250048 194264010876 35161828228800 6364290967005036 1151936658876177408 208500535086218801244 37738596847289464820928

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-3})$$.
All geometric endomorphisms are defined over $\F_{181}$.

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 1.181.ba $2$ (not in LMFDB) 1.181.h $3$ (not in LMFDB) 1.181.t $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 1.181.ba $2$ (not in LMFDB) 1.181.h $3$ (not in LMFDB) 1.181.t $3$ (not in LMFDB) 1.181.at $6$ (not in LMFDB) 1.181.ah $6$ (not in LMFDB)