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I'm about to read Mazur's paper "Modular curves and the Eisenstein ideal". It's so long and difficult for me, but I found a website which shows the Mazur's theorem. This is very short and very very easy comparing with the original paper.

Why is the original paper very long and difficult? Or equivalently, why is this website short and easy?

The original paper needs many advanced theory, for example, Katz's modular forms. But the website does not use this theory. And I think that there are more advanced theories which are used in the original paper, but are not in the website. What's happening?

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    $\begingroup$ The subject of these lectures is not the Modular curves and the Eisenstein ideal paper, but rather Mazur's subsequent and different proof of his rational torsion theorem. The (rather shorter) original paper this follows is, instead, Rational isogenies of prime degree, from Invent. math. 44 (1978), pp. 129-162. $\endgroup$
    – Vesselin Dimitrov
    Commented Nov 23, 2018 at 18:20
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    $\begingroup$ @VesselinDimitrov Thank you very much! I'll read it. $\endgroup$
    – k.j.
    Commented Nov 23, 2018 at 19:01

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