On the arithmetic of certain modular curves

Abstract

In this work, we estimate the genus of the intermediate modular curves between $X_1(N)$ and $X_0(N),$ and determine all the trigonal ones.

18 pages

References in corpus (2)

• d-gonality of modular curves and bounding torsions
• A linear lower bound on the gonality of modular curves

Cited by in corpus (11)

• Torsion of rational elliptic curves over quartic Galois number fields
• Bielliptic intermediate modular curves
• Torsion points on elliptic curves with complex multiplication
• Odd degree isolated points on $X_1(N)$ with rational $j$-invariant
• Intermediate modular curves with infinitely many cubic points over $\mathbb{Q}$
• A criterion to rule out torsion groups for elliptic curves over number fields
• Torsion points of elliptic curves over multi-quadratic number fields
• Weierstrass points at irregular cusps
• A note on the Kenku's method
• On the small cyclic torsion of elliptic curves over cubic number fields
• Hyperelliptic and trigonal modular curves in characteristic $p$