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 May 23 comment Finding Riemannian metric for this geodesic No, I think I misunderstood the question. May 23 comment Finding Riemannian metric for this geodesic These curves lie in a codimension 1 submanifold. For $d = 1$, $\gamma(t) \equiv 1$ Dec 21 comment Can the pre-image of the real points in the complex upper-half plane of a modular elliptic curve under the modular parametrization be identified? @ChrisWuthrich Ah, of course, thanks Dec 21 comment Can the pre-image of the real points in the complex upper-half plane of a modular elliptic curve under the modular parametrization be identified? @ChrisWuthrich Is it easy to see that complex conjugation corresponds to reflection in the imaginary axis? Dec 21 comment Can the pre-image of the real points in the complex upper-half plane of a modular elliptic curve under the modular parametrization be identified? Thanks Will! Do I understand correctly that this is what you're saying: you view $E$ as a quotient of the moduli space $X_0(N)$. Then the real locus maps to a real curve on $E(\Bbb C)$ with the property that the imaginary part of the invariant differential vanishes. On $\mathfrak H$ this differential is $2\pi if(\tau)d\tau$ up to a constant factor and the imaginary part of the differential vanishes on curves over which the imaginary part of the modular form is constant. Dec 21 comment Can the pre-image of the real points in the complex upper-half plane of a modular elliptic curve under the modular parametrization be identified? Thanks a lot! Indeed the formulation was very unclear, I meant points of $\mathfrak{H}$ corresponding to real points of $X_0(N)$ or mapping to real points of $E$. I edited the question to make it clearer. Dec 21 revised Can the pre-image of the real points in the complex upper-half plane of a modular elliptic curve under the modular parametrization be identified? minor edit Dec 21 awarded Student Dec 21 asked Can the pre-image of the real points in the complex upper-half plane of a modular elliptic curve under the modular parametrization be identified? May 19 awarded Yearling May 19 revised Hochschild cohomology and formal smoothness math typesetting May 19 suggested approved edit on Hochschild cohomology and formal smoothness Apr 28 awarded Necromancer Sep 23 answered Does the automorphism group of a cone determine the cone? May 6 answered Pythagorean 5-tuples Apr 27 answered probability and math puzzle books/references Nov 29 awarded Enthusiast Sep 7 awarded Supporter Sep 2 answered Experimental Mathematics Aug 9 comment Math puzzles for dinner Solution: Chg gur pbva rknpgyl va gur zvqqyr. Gura jurerire lbhe nqirefnel chgf gur pbva, chg vg ng gur fnzr cbfvgvba nsgre ebgngvba ol 180 qrterrf nebhaq gur pragre. (Guvf cbfvgvba vf nyjnlf serr).