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2021-08-28 11:48:14 +0200 asked a question How to radicalize `fraction * I` or `number * N^(± 1/2)`

How to radicalize $fraction * I \; , number* \{N}^{\pm \frac{1}{2}} $ There seem to be 2 cases which would help me to co

2021-08-28 11:44:09 +0200 asked a question How to radicalize $fraction * I \; , number* \{N}^{\pm \frac{1}{2}} $

How to radicalize $fraction * I \; , number* \{N}^{\pm \frac{1}{2}} $ There seem to be 2 cases which would help me to co

2021-02-05 01:17:18 +0200 received badge  Organizer (source)
2021-02-05 01:07:13 +0200 asked a question Elliptic curve $y^2 = x^3-n^2x$ large integral points

Hello ,

what can one expect for large n like the example below. The variable n is a composite with 114 digits. n %8 ==1

Can sage find integral points on this curve over Q?

n=583649461129466894559704245411893600602623703932428522192936531259527285468160111988363293313691731205609616721201 ax=[-n^2,0] E=EllipticCurve(QQ,ax)

2021-02-05 00:56:16 +0200 commented question Is the generator for $y^2=x^3-173^2*x$ wrong?

Hello I did not notice your question until just now,

this would be more logically to me: EN([x1,y1])= (-2367961190733987384484/13899676302553111225 : -20360870451358918327824797419314/51821147995950007613689182125 : 1)

because x1 is a square

you can verify this for example to be the case for other primes 5 mod 8

2021-01-30 13:18:47 +0200 received badge  Student (source)
2021-01-30 13:17:18 +0200 asked a question Is the generator for $y^2=x^3-173^2*x$ wrong?

n=173 E= EllipticCurve(QQ,[-n^2, 0]) PE= EN.gens() PE

[(-6346126062132248337293/4772605191075675626409 : -65772315471055459573813698990176860/329710868938260274308064195438827 : 1)]

I found a different solution.

2021-01-30 13:17:18 +0200 asked a question Is the generator for $y^2=x^3-173^2x$ wrong?

n=173 E= EllipticCurve(QQ,[-n^2, 0]) PE= EN.gens() PE [(-6346126062132248337293/4772605191075675626409 : -65772315471055459573813698990176860/329710868938260274308064195438827 : 1)]