Can mother transfer agricultural land to her name

A. No. If your father died without makeing a Will (Intestate), Your mother has 1/3 right over the agricultural land and remain children also are having 1/3 right over the agricultural land.

B. Therefore, your mother not only absolute owner of the agricultural land and deceased father children also have the right over the agricultural land. Hence, you can challenge the same before the Court under the Indian Sucession Act, 1925.

Thanks.  Please advise if the christian will has to be registered or not.

What do you mean by the christian will be registered or not?, You have been advised about the legality in detai by learned Mr. Ravi rferring to the Indian Successon Act, being a Christian this law will apply to you.  For further issues you may consult a local lawyer.