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:<math>y \mapsto y-\frac{(2y+1)(x^4+x^3-3x^2+3x-1)}{x^3(x-1)^3}</math>
and factor, we get an extraneous factor of a rational function of x, and the curve y^2+y=x^3-x^2, with j-invariant -4096/11. Hence both curves are modular of level 11, having mappings from X<sub>0</sup>(11).
By a theorem of [[Henri Carayol]], if an elliptic curve E is modular than its conductor, an isogeny invariant described originally in terms of [[cohomology]],
is the smallest integer n such that there exists a rational mapping φ:X<sub>0</sub>(n)</sub> → E. Since we now know all elliptic curves over '''Q''' are modular, we also know that the conductor is simply the level n of its minimal modular parametrization.
== Galois theory of the modular curve ==
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