## Experimental Mathematics

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

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

#### 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