Inverse Elliptic Curves Problem

[Artur]

Dear Jaap and other Seqfans
Yes I give x-coordinates of the integer points.
Elliptic equation is more general that reduced case y^2=x^3+n but I 
don't know exact form (if I will be know I will be don't ask)
I know only set of integer points x-coordinates and I also don't know 
that this set is complete or not. But only two cases can occured
1) set is complete only for positive values of x and can occured also 
other x but every time only with negative values
2)  set is complete
My problem is connected with Inverse Galois Theory but solved them can 
be used in many other branch of Mathematics.

Some times ago I was try push Neil Sloane to do additional base 
sequences with numebrs e.g. F inspite A which will be contains finite 
and short sequences. Engine will be that same as for ONEIS with A.
This base will be able to stored finite integer solutions of elliptic 
curves and will be possible to search e.g. 216, 418
I know many prooved and unprooved sequences in theory of numbers which 
contains 1, 2 and 3 numbers only. Because ONEIS is generally 
Encyclopedia  will be good that contain all knowledge from theory of 
number. I'm understand Neil point of  view that short common  sequences 
like 1, 2, 3 wil be almost not possible to find in recent base but will 
be do some terrible for working search function and from these reason I 
was suggested for Neil do separated base with other sumbols like 
F000001: 5186 :EulerPhi(n)=EulerPhi(n+1)=EulerPhi(n+2)
or F00002: 1,2,6 :such n that Fibbonacci(n) is cube
5,13,563 prime numbers of the form ((p-1)!+1)p
This F base will be appropriate place to stored base of solutions  
Elliptic curves

and the most important we will be celebrated  very soon 200k sequences

BEST WISHES
ARTUR









Jaap Spies pisze:
> Artur wrote:
>> Who know how find elliptic curve which have exactly that same set of 
>> solutiuon  as desired ? Any programme or idea ?
>> e.g. I need find elliptic curves which have only:
>>
>> single value:
>> {38}
>>
>> 2 values:
>> {1,3}
>> {216, 418}
>> {67, 576}
>>
>> 3 values:
>> {3,5,7}
>> {105, 147, 273}
>> {715, 915, 1029}
>>
>> 4 values:
>> {3, 6, 7, 13}
>> {32, 48, 158, 168}
>>
>> 5 values:
>>
>> {84, 471, 1836, 2444, 4187}
>>
>> ARTUR
>>
>>
>>
>>
>
> Your answer shed some light on your question:
>
>> Dear Jaap,
>> For many elliptic curves you have finite set of integer solutions
>> see
>> http://www.research.att.com/~njas/sequences/?q=Jasinski+Elliptic&language=english&go=Search 
>>
>> If  you have explicit fom of elliptic curve you can find set of  
>> integer solution
>> my question is possible finding elliptic curve if we know set of 
>> integer points
>> BEST WISHES
>> ARTUR
>>
>>
>> Jaap Spies pisze:
>>> Artur wrote:
>>>> Who know how find elliptic curve which have exactly that same set 
>>>> of solutiuon  as desired ? Any programme or idea ?
>>>> e.g. I need find elliptic curves which have only:
>>>>
>>>
>>> I do not understand your question. Can you give more information?
>>>
>>> Jaap
>>>
>
> Are you talking about a special kind of elliptic curves? y^2 = x^3 + n?
> Or??
>
> And you give x-coordinates of the integer points?
>
> Do you have the corresponding y values?
>
> It is still not clear what you want to find.
>
> Regards,
>
> Jaap
>
>
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