Invariants
Level: | $240$ | $\SL_2$-level: | $48$ | Newform level: | $1$ | ||
Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
Genus: | $9 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (of which $2$ are rational) | Cusp widths | $6^{4}\cdot12^{2}\cdot48^{2}$ | Cusp orbits | $1^{2}\cdot2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $3 \le \gamma \le 9$ | ||||||
$\overline{\Q}$-gonality: | $3 \le \gamma \le 9$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 48A9 |
Level structure
$\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}3&4\\160&229\end{bmatrix}$, $\begin{bmatrix}61&68\\128&41\end{bmatrix}$, $\begin{bmatrix}97&18\\144&85\end{bmatrix}$, $\begin{bmatrix}123&208\\224&105\end{bmatrix}$, $\begin{bmatrix}169&132\\24&181\end{bmatrix}$, $\begin{bmatrix}177&214\\40&61\end{bmatrix}$, $\begin{bmatrix}213&34\\152&165\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.144.9.b.1 for the level structure with $-I$) |
Cyclic 240-isogeny field degree: | $48$ |
Cyclic 240-torsion field degree: | $3072$ |
Full 240-torsion field degree: | $1966080$ |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
24.144.4-24.ch.1.38 | $24$ | $2$ | $2$ | $4$ | $0$ |
240.96.1-240.a.2.6 | $240$ | $3$ | $3$ | $1$ | $?$ |
240.144.4-24.ch.1.14 | $240$ | $2$ | $2$ | $4$ | $?$ |
240.144.4-240.cn.1.50 | $240$ | $2$ | $2$ | $4$ | $?$ |
240.144.4-240.cn.1.79 | $240$ | $2$ | $2$ | $4$ | $?$ |
240.144.5-240.e.1.50 | $240$ | $2$ | $2$ | $5$ | $?$ |
240.144.5-240.e.1.79 | $240$ | $2$ | $2$ | $5$ | $?$ |