Timeline for Are there nonisotrivial elliptic curves over $\mathbb{G}_m$?

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when toggle format	what		by	license	comment
Dec 12, 2014 at 19:48	comment	added	Lisa S.		Thank you. Why does the image of Galois induce a $p$-cycle ramified above the pole of $j_E$ (and what does that mean)?
Dec 12, 2014 at 5:11	comment	added	Noam D. Elkies		There might not be an entirely simple proof of this result. The nonconstant elliptic curves over ${\mathbb C}^*$ are quadratic twists $y^2 = x^3 + at x^2 + bt^2 x + ct^3$, cubic twists $y^2 = x^3 + at^2$ and $y^2 = x^3 + at^4$, quartic twists $y^2 = x^3 + at x$ and $y^2 = x^3 + at^3 x$, and sextic twists $y^2 = x^3 + at$ and $y^2 = x^3 + at^5$; any argument must account for all of these. The proof I gave is conceptual but advanced; the Szpiro path is elementary (Szpiro is basically Mason = polynomial ABC) but requires case analysis.
Dec 12, 2014 at 4:38	history	answered	Noam D. Elkies	CC BY-SA 3.0