Experimental Mathematics

Rational points on {$X\sb 0\sp +(p)$}

Steven D. Galbraith

Abstract

We study the rational points on $X_0^+(p) = X_0(p) / W_p$. It is known that there are rational points corresponding to cusps and elliptic curves with complex multiplication (CM). We use computational methods to exhibit exceptional rational points on $X_0^+(p)$ for p = 73, 103, 137, 191 and 311. We also provide the j-invariants of the corresponding non-CM quadratic $\funnyQ$-curves.

Article information

Source
Experiment. Math., Volume 8, Issue 4 (1999), 311-318.

Dates
First available in Project Euclid: 9 March 2003

Permanent link to this document
https://projecteuclid.org/euclid.em/1047262354

Mathematical Reviews number (MathSciNet)
MR1737228

Zentralblatt MATH identifier
0960.14010

Subjects
Primary: 11G18: Arithmetic aspects of modular and Shimura varieties [See also 14G35]
Secondary: 11F11: Holomorphic modular forms of integral weight

Keywords
modular curves Heegner points $\funnyQ$-curves

Citation

Galbraith, Steven D. Rational points on {$X\sb 0\sp +(p)$}. Experiment. Math. 8 (1999), no. 4, 311--318. https://projecteuclid.org/euclid.em/1047262354


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