I have this quartic which I want to change into a Weierstrass elliptic curve :
$$v^2 = (p^4 - 2p^3 + 5p^2 + 8p + 4)$$
and I found a different elliptic curve to the one in the book and was told that they are the same by some change of variable.
I found: $y^2=x^3-(121/3)x-1690/27$.
Book : $y^2 = x^3-3267x+45630$
How is that even possible. I tried scaling through with a factor of 81 (by looking at the coefficient of $x$), but it did not help. Can someone help me drop few hints?
In the book :
My calculation by using Maple :
I noticed and tried playing around with the change of variable because they look almost the same with a difference in the constant term with no luck. Can someone help me indicate why these are different yet the same. Thank you.