Singular points on a variety. $V: 4x^2y^2=(x^2+y^2)^3$
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So I was studying some stuff about projective varieties from the book "The Arithmetic of Elliptic Curves" from Silverman, and there is this exercise at the very beginning, about determine the singular points of $$V: 4x^2y^2=(x^2+y^2)^3$$ I got the points $(0,0)$ and $(pm1/sqrt{3},pm1/sqrt{3})$ (the 4 possible combinations), which is ok but, none of the $(pm1/sqrt{3},pm1/sqrt{3})$ belong to the curve, so I'm curious about what do they mean, if they happen to mean anything. Thanks.
elliptic-curves affine-varieties
asked Dec 1 '18 at 19:56
Cristian BaezaCristian Baeza
420213
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add a comment |
$begingroup$
So I was studying some stuff about projective varieties from the book "The Arithmetic of Elliptic Curves" from Silverman, and there is this exercise at the very beginning, about determine the singular points of $$V: 4x^2y^2=(x^2+y^2)^3$$ I got the points $(0,0)$ and $(pm1/sqrt{3},pm1/sqrt{3})$ (the 4 possible combinations), which is ok but, none of the $(pm1/sqrt{3},pm1/sqrt{3})$ belong to the curve, so I'm curious about what do they mean, if they happen to mean anything. Thanks.
elliptic-curves affine-varieties
asked Dec 1 '18 at 19:56
Cristian BaezaCristian Baeza
420213
$endgroup$
add a comment |
$begingroup$
So I was studying some stuff about projective varieties from the book "The Arithmetic of Elliptic Curves" from Silverman, and there is this exercise at the very beginning, about determine the singular points of $$V: 4x^2y^2=(x^2+y^2)^3$$ I got the points $(0,0)$ and $(pm1/sqrt{3},pm1/sqrt{3})$ (the 4 possible combinations), which is ok but, none of the $(pm1/sqrt{3},pm1/sqrt{3})$ belong to the curve, so I'm curious about what do they mean, if they happen to mean anything. Thanks.
elliptic-curves affine-varieties
asked Dec 1 '18 at 19:56
Cristian BaezaCristian Baeza
420213
$endgroup$
So I was studying some stuff about projective varieties from the book "The Arithmetic of Elliptic Curves" from Silverman, and there is this exercise at the very beginning, about determine the singular points of $$V: 4x^2y^2=(x^2+y^2)^3$$ I got the points $(0,0)$ and $(pm1/sqrt{3},pm1/sqrt{3})$ (the 4 possible combinations), which is ok but, none of the $(pm1/sqrt{3},pm1/sqrt{3})$ belong to the curve, so I'm curious about what do they mean, if they happen to mean anything. Thanks.
elliptic-curves affine-varieties
elliptic-curves affine-varieties
asked Dec 1 '18 at 19:56
Cristian BaezaCristian Baeza
420213
asked Dec 1 '18 at 19:56
Cristian BaezaCristian Baeza
420213
asked Dec 1 '18 at 19:56
Cristian BaezaCristian Baeza
420213
asked Dec 1 '18 at 19:56
Cristian BaezaCristian Baeza
420213
asked Dec 1 '18 at 19:56
Cristian BaezaCristian Baeza
420213
420213
add a comment |
add a comment |
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