I am currently in my first year of a general mathematics PhD program at a state university that isn't rated particularly high. As far my classes go, I put in little to no effort towards them and instead dedicate my time to the research I've started, and still am at/near the top of my class. The students in my classes just seem to be at a much lower level of understanding than I am, and I am afraid I am stagnating myself by not being in a more competitive setting. I've begun working on a research project with a few other students who are soon to graduate, and thus far, everything we have done this semester has come from me, even though I haven't even finished the sequence of courses relevant to the material we are researching. Granted, there are a few professors who are well-respected in their field that I currently work under, and that is a great privilege, but I do not feel that most the other students there are my academic peers.
I would like to look into transferring to a better university, but I have one main concern; my undergraduate transcript is not very good. Upon close inspection, one would find that I received very good grades in the advanced classes I took, but poor grades in the easier classes I took earlier in my academic career. I got a 4.0 the first semester of my grad program, and am confident that I will 4.0 this semester as well, but will this be enough to get into a highly ranked PhD program?(Edit: This is a rhetorical question, not the question I am trying to ask. It is obvious that this is not enough, so I am trying to find out what outside of this I can do?)
So my question is should I look into transferring?(and maybe risk offending the professors I have a good relationship right now?) and if so how can I prove that what they see on paper(my undergraduate transcript) is not reflective of my abilities as a mathematician?
EDIT: I should mention that my biggest concern right now is that my classes are being held back by the people who don't understand the material. I would love to be in a class where things were faster-paced so we could get into more detail and more subjects. I've been studying into more detail by myself, but I feel I would benefit from seeing this from my instructor as well(which is what I would imagine happens at a university with a better student body), which I don't get because too many people in my classes are struggling with the basics.