Invariants
Level: | $240$ | $\SL_2$-level: | $16$ | ||||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (none of which are rational) | Cusp widths | $2^{8}\cdot16^{2}$ | Cusp orbits | $2^{5}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $1 \le \gamma \le 2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16G0 |
Level structure
$\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}61&168\\207&239\end{bmatrix}$, $\begin{bmatrix}95&136\\167&69\end{bmatrix}$, $\begin{bmatrix}103&184\\26&51\end{bmatrix}$, $\begin{bmatrix}137&200\\207&59\end{bmatrix}$, $\begin{bmatrix}145&184\\78&217\end{bmatrix}$, $\begin{bmatrix}211&112\\219&37\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.48.0.m.1 for the level structure with $-I$) |
Cyclic 240-isogeny field degree: | $48$ |
Cyclic 240-torsion field degree: | $1536$ |
Full 240-torsion field degree: | $5898240$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
16.48.0-8.q.1.2 | $16$ | $2$ | $2$ | $0$ | $0$ |
120.48.0-8.q.1.2 | $120$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-240.n.1.2 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-240.n.1.31 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-240.n.1.34 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-240.n.1.63 | $240$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.