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Question: Elliptic curves

Question:Elliptic curves

Alfred_F 425 Maple
number-theory
3 hours ago
0

Having started learning Maple about a year ago as a beginner, and now having mastered my preferred area of ​​"ordinary differential equations" fairly independently, I'd like to explore "elliptic curves" in Maple. For practice, I've chosen two problems, for each of which I only know one solution:

y^2 = x^3  -51*x^2 + 867*x - 4792    (17;11)

y^2 - 2*y + 14 = 2*x^3 + 11*x^2 - 29*x - 17    (3;7)


My attempts using commands like "algcurves", "ThueSolve", and "parametrization" have failed. How does one approach such problems in Maple? I'm also particularly interested in the group-theoretically based graphical secant method.

(I'm familiar with the book by Silverman/Tate.)
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