question on recovering a single parameter from a minimal model elliptic curve

[American Citizen <website.reader3@gmail.com>]

Hi:

I have an elliptic curve (not minimal model) defined for a rational 
number r.

> ? r = 33/29
> ? E1(x)[1..5]
> %12 = [(-4*x^4 + 8*x^2 - 4)/(x^4 + 4*x^3 + 2*x^2 - 4*x + 1), (4*x^6 - 
> 8*x^5 - 12*x^4 + 16*x^3 + 12*x^2 - 8*x - 4)/(x^6 + 6*x^5 + 9*x^4 - 
> 4*x^3 - 9*x^2 + 6*x - 1), (16*x^10 - 32*x^9 - 80*x^8 + 128*x^7 + 
> 160*x^6 - 192*x^5 - 160*x^4 + 128*x^3 + 80*x^2 - 32*x - 16)/(x^10 + 
> 10*x^9 + 35*x^8 + 40*x^7 - 30*x^6 - 68*x^5 + 30*x^4 + 40*x^3 - 35*x^2 
> + 10*x - 1), (48*x^14 - 96*x^13 - 336*x^12 + 576*x^11 + 1008*x^10 - 
> 1440*x^9 - 1680*x^8 + 1920*x^7 + 1680*x^6 - 1440*x^5 - 1008*x^4 + 
> 576*x^3 + 336*x^2 - 96*x - 48)/(x^14 + 14*x^13 + 77*x^12 + 196*x^11 + 
> 161*x^10 - 238*x^9 - 427*x^8 + 184*x^7 + 427*x^6 - 238*x^5 - 161*x^4 + 
> 196*x^3 - 77*x^2 + 14*x - 1), (-64*x^20 + 256*x^19 + 384*x^18 - 
> 2304*x^17 - 832*x^16 + 9216*x^15 + 512*x^14 - 21504*x^13 + 896*x^12 + 
> 32256*x^11 - 1792*x^10 - 32256*x^9 + 896*x^8 + 21504*x^7 + 512*x^6 - 
> 9216*x^5 - 832*x^4 + 2304*x^3 + 384*x^2 - 256*x - 64)/(x^20 + 20*x^19 
> + 170*x^18 + 780*x^17 + 1965*x^16 + 2064*x^15 - 1800*x^14 - 6480*x^13 
> - 1710*x^12 + 8600*x^11 + 3772*x^10 - 8600*x^9 - 1710*x^8 + 6480*x^7 - 
> 1800*x^6 - 2064*x^5 + 1965*x^4 - 780*x^3 + 170*x^2 - 20*x + 1)]
> ? E1(r)[1..5]
> %13 = [-61504/1168561, -51232832/1263214441, 
> -3151024099328/1476143130389401, 
> -145350439653801984/1724963292590968821961, 
> -2482238218636458402512896/2178998541395820122081893138801]
> ? E1_min(r)[1..5]
> %14 = [0, -1, 0, -274977905984, -55446464208117696]
Given the minimal model E1_min coefficients, how can I recover r = 33/29?

This is like forward/reverse from parameter to curve, then from minimal 
model curve back to parameter.

Occasionally I have curves lying around and I need to recover the 
parameter that created it.

Randall