Dear All,
Let $C$ be the following curve in $\mathbb{C}^2$.
\begin{align}
& 11664 {c_1}^3 {c_2}^2 + 536544 {c_1}^3 c_2 + 6170256 {c_1}^3 + 67068
{c_1}^2 {c_2}^2 + 1542564 {c_1}^2 c_2 \\
& + 3085128 c_1 {c_2}^2 - 32393844 c_1 c_2 + 3085128 c_1 + 17739486 {c_2}^2
+ 6941538 c_2 = 0.
\end{align}
I checked that this curve has genus $1$ using Sage. Therefore it is an
elliptic curve. How to change coordinates such that the equation of this
curve is of the form $y^2 = f(x)$, where $f$ is some polynomial. Thank you
very much.
I tried to use the following codes in Sage.
R.<c1,c2> = QQ[]; Jacobian(11664*c1^3*c2^2 + 536544*c1^3*c2 + 6170256*c1^3
+ 67068*c1^2*c2^2 + 1542564*c1^2*c2 + 3085128*c1*c2^2 - 32393844*c1*c2 +
3085128*c1 + 17739486*c2^2 + 6941538*c2)
But there is an error: NoEmbeddingError: not a sub-polytope of a reflexive
polygon.
How to find the normal form of this curve using Sage? Thank you very much.
Best regards,
Jianrong.
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