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 | $2^{4}\cdot4^{2}\cdot8^{4}$ | Cusp orbits | $2^{5}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8O0 |
Level structure
$\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}17&184\\154&91\end{bmatrix}$, $\begin{bmatrix}25&224\\32&9\end{bmatrix}$, $\begin{bmatrix}29&232\\56&51\end{bmatrix}$, $\begin{bmatrix}55&24\\218&215\end{bmatrix}$, $\begin{bmatrix}197&80\\108&221\end{bmatrix}$, $\begin{bmatrix}201&184\\166&87\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.48.0.da.1 for the level structure with $-I$) |
Cyclic 240-isogeny field degree: | $48$ |
Cyclic 240-torsion field degree: | $1536$ |
Full 240-torsion field degree: | $5898240$ |
Rational points
This modular curve has no real points, and therefore no 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.i.1.2 | $16$ | $2$ | $2$ | $0$ | $0$ |
240.48.0-8.i.1.2 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-120.ej.2.2 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-120.ej.2.6 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-120.ej.2.27 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-120.ej.2.31 | $240$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.