Given the following elliptic curve y2 ≡ x3 + 2x + 5 mod 11, answer the following: Confirm that it is an elliptic curve What are the lower and upper bounds on the number of integer points on this curve? (Hint: Use Hasse's theorem) Find the double of the point (3,4) on this curve. Find the addition of points (3,4) and (8,4) on this curve.
Given the following elliptic curve y2 ≡ x3 + 2x + 5 mod 11, answer the following: Confirm that it is an elliptic curve What are the lower and upper bounds on the number of integer points on this curve? (Hint: Use Hasse's theorem) Find the double of the point (3,4) on this curve. Find the addition of points (3,4) and (8,4) on this curve.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 63RE
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Question
Given the following elliptic curve y2 ≡ x3 + 2x + 5 mod 11, answer the following:
Confirm that it is an elliptic curve
What are the lower and upper bounds on the number of integer points on this curve? (Hint: Use Hasse's theorem)
Find the double of the point (3,4) on this curve.
Find the addition of points (3,4) and (8,4) on this curve.
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