2
votes
1answer
64 views

History of the Coefficients of Elliptic Curves — Why $a_6$? [duplicate]

I would like to know what is the motivation behind the naming convention of the Weierstrass form of elliptic curves given as $$E:y^2+a_1xy+a_3y=x^3+a_2x^2+a_4x+a_6.$$ I can see that $a_1,a_2,a_3,a_4$ ...
2
votes
2answers
69 views

Reason behind standard names of coefficients in long Weierstrass equation

A long Weierstrass equation is an equation of the form $$y^2+a_1xy+a_3y=x^3+a_2x^2+a_4x+a_6$$ Why are the coefficients named $a_1, a_2, a_3, a_4$ and $a_6$ in this manner, corresponding to $xy, x^2, ...
4
votes
1answer
137 views

Mathematics for Pleasure of a Beginner

I've just read "The Music of the Primes" by Marcus du Sautoy, it is worth a read. I'm not from a maths background, but I'd like to develop a deeper understanding of the concepts. The poetry of math is ...
12
votes
3answers
961 views

History of elliptic curves

In one sense elliptic curves are a rather modern object as some of its properties have been studied only in the last century or so. But in another sense there are a very classical object for studying ...
3
votes
1answer
579 views

Reference request for “Weierstrass equation” and “Weierstrass normal form”

I would like to know more about the history of the widely used terms "Weierstrass equation" and "Weierstrass normal form", as they appear in the theory of elliptic curves. When were these terms first ...
0
votes
1answer
364 views

Resurrection of my Tamagawa numbers Question, to understand the Formulation of BSD

My previous question was closed very badly for asking the broad and deep things, so I now understand the consequences of asking such questions, so I refrain from asking such questions, so this is not ...