## Experimental Mathematics

### Computing the Level of a Modular Rigid Calabi-Yau Threefold

Luis V. Dieulefait

#### Abstract

In a previous article (see Dieulefait and Manoharmayum), the modularity of a large class of rigid Calabi-Yau threefolds was established. To make that result more explicit, we recall (and reprove) a result of Serre giving a bound for the conductor of "integral" two-dimensional compatible families of Galois representations and apply this result to give an algorithm that determines the level of a modular rigid Calabi-Yau threefold. We apply the algorithm to three examples.

#### Article information

Source
Experiment. Math., Volume 13, Issue 2 (2004), 165-170.

Dates
First available in Project Euclid: 20 July 2004

https://projecteuclid.org/euclid.em/1090350931

Mathematical Reviews number (MathSciNet)
MR2068890

Zentralblatt MATH identifier
1060.14059

Subjects
Primary: 14J30: $3$-folds [See also 32Q25]
Secondary: 11F23: Relations with algebraic geometry and topology

#### Citation

Dieulefait, Luis V. Computing the Level of a Modular Rigid Calabi-Yau Threefold. Experiment. Math. 13 (2004), no. 2, 165--170. https://projecteuclid.org/euclid.em/1090350931