Re: [sage-support] Re: Writing a particular Elliptic Curve

[Bhavin Moriya]

Thanks Peter.





*Bhavin K Moriya  NASI
Research AssociateHarish Chandra Research Institute
*
*Chhatnag Road, Jhusi*
*Allahabad - 211 019.*

"Only the gentle are ever really strong."
- James Dean





On Thu, Apr 10, 2014 at 7:12 PM, Peter Bruin  wrote:

> Dear Bhavin,
>
>
> Thank you very much for your answer. It helps but still I do not know how
>> to see the answer to my exact problem.
>> My exact problem is the see the graph of y^2=x(x+1)(2*x+1)/6.
>>
>
> If you have constructed an elliptic curve (after scaling the variables),
> say E, then you can do
>
> sage: E.plot()
>
> Otherwise, you can try something like
>
> sage: R.=RR[]
> sage: f=y^2-x*(x+1)*(2*x+1)/6
> sage: C=Curve(f)
> sage: C.plot()
>
> Peter
>
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[sage-support] Re: Writing a particular Elliptic Curve

[Peter Bruin]

Dear Bhavin,

Thank you very much for your answer. It helps but still I do not know how 
> to see the answer to my exact problem.
> My exact problem is the see the graph of y^2=x(x+1)(2*x+1)/6. 
>

If you have constructed an elliptic curve (after scaling the variables), 
say E, then you can do

sage: E.plot()

Otherwise, you can try something like

sage: R.=RR[]
sage: f=y^2-x*(x+1)*(2*x+1)/6
sage: C=Curve(f)
sage: C.plot()

Peter

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[sage-support] Re: Writing a particular Elliptic Curve

[Bhavin Moriya]

Dear Peter,

Thank you very much for your answer. It helps but still I do not know how 
to see the answer to my exact problem.
My exact problem is the see the graph of y^2=x(x+1)(2*x+1)/6. 

On Thursday, April 10, 2014 6:58:13 PM UTC+5:30, Peter Bruin wrote:
>
> Hello,
>
> Sage only supports equations where the coefficients of y^2 and x^3 are 1; 
> you first need to multiply the equation by A^2 and then put A*y = Y and A*x 
> = X, so the equation becomes
>
> Y^2 = X^3 + B*X^2 + A*C*X + A^2*D
>
> You can construct this (assuming A, B, C, D are set to suitable values) 
> using
>
> sage: E = EllipticCurve([0, B, 0, A*C, A^2*D])
>
> I hope this answers your question.
>
> Peter
>
>
> Op donderdag 10 april 2014 07:25:15 UTC+1 schreef Bhavin Moriya:
>>
>> How do I write the following elliptic curve in SAGE,
>>
>> y^2 = A*x^3 + B*x^2 + C*x + D?
>>
>

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[sage-support] Re: Writing a particular Elliptic Curve

[Peter Bruin]

Hello,

Sage only supports equations where the coefficients of y^2 and x^3 are 1; 
you first need to multiply the equation by A^2 and then put A*y = Y and A*x 
= X, so the equation becomes

Y^2 = X^3 + B*X^2 + A*C*X + A^2*D

You can construct this (assuming A, B, C, D are set to suitable values) 
using

sage: E = EllipticCurve([0, B, 0, A*C, A^2*D])

I hope this answers your question.

Peter


Op donderdag 10 april 2014 07:25:15 UTC+1 schreef Bhavin Moriya:
>
> How do I write the following elliptic curve in SAGE,
>
> y^2 = A*x^3 + B*x^2 + C*x + D?
>

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