# Properties

 Label 1.61.am Base Field $\F_{61}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{61}$ Dimension: $1$ L-polynomial: $1 - 12 x + 61 x^{2}$ Frobenius angles: $\pm0.221142061624$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-1})$$ Galois group: $C_2$ Jacobians: 3

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 3 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 50 3700 227450 13852800 844651250 51520609300 3142742303450 191707292275200 11694145876656050 713342910332792500

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 50 3700 227450 13852800 844651250 51520609300 3142742303450 191707292275200 11694145876656050 713342910332792500

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-1})$$.
All geometric endomorphisms are defined over $\F_{61}$.

## 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 1.61.m $2$ (not in LMFDB) 1.61.ak $4$ (not in LMFDB) 1.61.k $4$ (not in LMFDB)