How to use gamma glm (with the fixed shape parameter) in R?

The reference is this website: The `family` Argument for `glmnet` • glmnet

It says

glmnet can fit penalized GLMs for any family as long as the family can be expressed as a family object. In fact, users can make their own families, or customize existing families, just as they can for regular GLMs.

Now I need to create my own family. It's gamma family with the shape parameter is fixed at 1. And the link function is standard log function.

I try this code first:

cv.glmnet(x=as.matrix(all_datasets[,c("V1","V2")]), y=all_datasets$V4, family= Gamma(link="log"), 
    type.measure = "mse", alpha = 1, nlambda = 100)

The above code works. But I am not sure whether its shape parameter is fixed at 1. The tutorial on the website lack the clear relevant information.