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edit approved Aug 10 at 1:25
Ali Taghavi
edit approved Aug 10 at 1:25
Ali Taghavi
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Camilo Gallardo
Camilo Gallardo
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I'm not sure whether this is obvious or not. If I remember correctly, theThe curve $X(1)$ parametrices all elliptic curves up to isomorphism class over $\mathbb{ C}$, and a $K$-rational point corresponds to an elliptic curve whose $j$-invariant lies in $K$, andbut if I remember correctly the $K$-rational points actually classify elliptic curves up to isomorphism over $K$. Is there an obvious reason for this?

I'm not sure whether this is obvious or not. If I remember correctly, the curve $X(1)$ parametrices all elliptic curves up to isomorphism class over $\mathbb{ C}$, and a $K$-rational point corresponds to an elliptic curve whose $j$-invariant lies in $K$, and the $K$-rational points actually classify elliptic curves up to isomorphism over $K$. Is there an obvious reason for this?

I'm not sure whether this is obvious or not. The curve $X(1)$ parametrices all elliptic curves up to isomorphism class over $\mathbb{ C}$, and a $K$-rational point corresponds to an elliptic curve whose $j$-invariant lies in $K$, but if I remember correctly the $K$-rational points actually classify elliptic curves up to isomorphism over $K$. Is there an obvious reason for this?

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Camilo Gallardo
Camilo Gallardo
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Do rational points on $X(1)$ correspond to elliptic curves up to rational isomorphism?

I'm not sure whether this is obvious or not. If I remember correctly, the curve $X(1)$ parametrices all elliptic curves up to isomorphism class over $\mathbb{ C}$, and a $K$-rational point corresponds to an elliptic curve whose $j$-invariant lies in $K$, and the $K$-rational points actually classify elliptic curves up to isomorphism over $K$. Is there an obvious reason for this?