See the File, working on topic 9.
9. Elliptic Curves over a field. Number Theory. Algebra. Does an elliptic curve have anything to do with an ellipse? Many interesting questions in number theory can be rephrased in the language of finding rational points on elliptic curves. Define the group associated with the rational points on an elliptic curve and give an example of calculating it; also explain finite elliptic curves as well. Explain the statements and consequences of important related ideas such as the Birch Swinnerton Dyer Conjecture or the Modularity Theorem.
A key part of this outline is articulating a main idea or main point that all the rest of paper should support. This is usually some key theorem, application, or perspective that you want to built up towards.
A good title for your topic
A good abstract (using the abstract environment in LaTeX)
A clearly articulated “main point” that you are framing your paper around. All of your paper should be in service of your main point.
Good use of sections
Good idea of what will be included in those sections (what are you defining, what lemmas/theorems are you including, what examples are you including)
Identification of what lemma/theorems you will prove.For more information on
check on this :https://en.wikipedia.org/wiki/Elliptic_curve
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