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Results tagged with elliptic-curves
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user 65
An elliptic curve is an algebraic curve of genus one with some additional properties. Questions with this tag will often have the top-level tags nt.number-theory or ag.algebraic-geometry. Note also the tag arithmetic-geometry as well as some related tags such as rational-points, abelian-varieties, heights. Please do not use this tag for questions related to ellipses; instead use conic-sections.
14
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Why is an elliptic curve a group?
Short answer: because it's a complex torus. Explanation below would take as through many topics.
Topological covers
The curve should be considered over complex numbers, where it can be seen as a Rie …
- 15.1k
11
votes
2
answers
1k
views
Elliptic curve over spectra?
Filling the gaps in my knowledge to understand the tmf question.
So, what is the analogue of elliptic curve over the category of spectra?
- 15.1k
8
votes
2
answers
8k
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What does "supersingular" mean?
Are supersingular primes and supersingular elliptic curves related?
(this was essentially a subquestion in my earlier question, but still looks sufficiently different to me to deserve a separate post …
- 15.1k
1
vote
Definition and meaning of the conductor of an elliptic curve
I don't find the definition of a conductor clunky.
Consider any fibration f: X \to Y, just between the algebraic varieties for now. Let's say we want to study it somehow in algebraic geometry. One o …
- 15.1k
0
votes
Sections of a divisor on elliptic curve
I would try to play with rational functions of the form xn/Q1Q2, perhaps they will form a big part of a basis?
- 15.1k
7
votes
1
answer
711
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Ways to characterize supersingular primes?
I've read the definition, and it basically says p is a supersingular prime iff
the fundamental domain of a group generated by \Gamma(p) and a matrix ((0, 1), (-p, 0)) is rational.
And there's a fini …
- 15.1k
12
votes
4
answers
2k
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Mystery of the Monstrous Moonshine
There's a very famous group, the largest sporadic simple finite group, sometimes called a monster whose size is quoted below. What's the explanation that the primes appearing in it,
#{Monster} = 2 …
- 15.1k