An elliptic curve is a curve of the form y^2 = x^3 + ax + b for some constants a, b. These curves are extremely special in that they admit an addition given by the following picture: P R P+Q P Q R=0 Addition of distinct points T P TOT=0 R ΡΘΡ Adding a point to itself (a) Verify that the point (-4, -3) lies on the curve y^2 = x^3 + 73. (b) Compute the sum (-4, -3) + (-4, -3) using the description and picture above. Verify that this point is also on the curve.

An elliptic curve is a curve of the form y^2 = x^3 + ax + b for some constants a, b. These curves are extremely special in that they admit an addition given by the following picture: P R P+Q P Q R=0 Addition of distinct points T P TOT=0 R ΡΘΡ Adding a point to itself (a) Verify that the point (-4, -3) lies on the curve y^2 = x^3 + 73. (b) Compute the sum (-4, -3) + (-4, -3) using the description and picture above. Verify that this point is also on the curve.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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