|October 26th, 2014, 12:26 AM||#1|
Joined: Sep 2014
elliptic curve symmetry and derivative
I was given the formula: y^2 = x^3 +ax +b ; where a and b are constants.
For the first question,
it asks me to prove that the elliptic curve is symmetric about the x-axis. I drew a diagram and my answer is that all points on the curve are the same total distance away from both foci. Therefore, if (x,y) is flipped about the x axis, it becomes (x, -y) and it is also on the curve, and the same distance away from both foci.
For the second question, it asks me to find dy/dx for the elliptic curve formula provided.
I come to dy/dx = (3x+a) / (2y)
Are my answers correct? If not how can I approach this differently?
|October 27th, 2014, 06:59 PM||#2|
Joined: May 2007
First question: for each x there are two values of which are equal in magnitude and opposite sign.
Second question: the answer is incomplete. You should substitute the formula for y into the expresion, noting that there are two values, so the derivative has two values - not surprising since the curve has two branches.
|October 27th, 2014, 08:13 PM||#3|
Joined: May 2013
From: The Astral plane
Math Focus: Wibbly wobbly timey-wimey stuff.
|curve, derivative, elliptic, symmetry|
|Search tags for this page|
Click on a term to search for related topics.
|Thread||Thread Starter||Forum||Replies||Last Post|
|Elliptic curve over finite field||Kentut||Number Theory||1||April 9th, 2014 06:03 AM|
|symmetry||mared||Algebra||1||January 27th, 2014 07:52 AM|
|Equation of a drawn line tangent to elliptic curve||Singularity||Calculus||1||December 12th, 2012 10:30 AM|
|Curve Sketching: First-Derivative Test||cokipoon||Calculus||2||March 19th, 2012 12:07 AM|
|Supersingular elliptic curve question||fathwad||Number Theory||3||June 2nd, 2007 11:19 AM|