Invariants
Level: | $240$ | $\SL_2$-level: | $80$ | Newform level: | $1$ | ||
Index: | $480$ | $\PSL_2$-index: | $240$ | ||||
Genus: | $16 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (none of which are rational) | Cusp widths | $5^{4}\cdot10^{2}\cdot20^{2}\cdot80^{2}$ | Cusp orbits | $2^{3}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $4 \le \gamma \le 30$ | ||||||
$\overline{\Q}$-gonality: | $4 \le \gamma \le 16$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 80B16 |
Level structure
$\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}0&73\\53&204\end{bmatrix}$, $\begin{bmatrix}63&218\\136&73\end{bmatrix}$, $\begin{bmatrix}77&16\\92&89\end{bmatrix}$, $\begin{bmatrix}148&109\\53&36\end{bmatrix}$, $\begin{bmatrix}197&236\\208&113\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.240.16.dz.2 for the level structure with $-I$) |
Cyclic 240-isogeny field degree: | $48$ |
Cyclic 240-torsion field degree: | $1536$ |
Full 240-torsion field degree: | $1179648$ |
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 |
---|---|---|---|---|---|
80.240.8-80.t.2.15 | $80$ | $2$ | $2$ | $8$ | $?$ |
120.240.8-120.gi.2.19 | $120$ | $2$ | $2$ | $8$ | $?$ |
240.96.0-240.cx.1.4 | $240$ | $5$ | $5$ | $0$ | $?$ |
240.240.8-80.t.2.29 | $240$ | $2$ | $2$ | $8$ | $?$ |
240.240.8-240.u.1.61 | $240$ | $2$ | $2$ | $8$ | $?$ |
240.240.8-240.u.1.62 | $240$ | $2$ | $2$ | $8$ | $?$ |
240.240.8-120.gi.2.31 | $240$ | $2$ | $2$ | $8$ | $?$ |