Invariants
Level: | $240$ | $\SL_2$-level: | $80$ | Newform level: | $1$ | ||
Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
Genus: | $7 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (of which $4$ are rational) | Cusp widths | $2^{4}\cdot8^{2}\cdot10^{4}\cdot40^{2}$ | Cusp orbits | $1^{4}\cdot2^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 7$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 7$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 40O7 |
Level structure
$\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}7&20\\112&93\end{bmatrix}$, $\begin{bmatrix}23&180\\199&227\end{bmatrix}$, $\begin{bmatrix}37&180\\220&119\end{bmatrix}$, $\begin{bmatrix}81&220\\128&63\end{bmatrix}$, $\begin{bmatrix}113&80\\165&163\end{bmatrix}$, $\begin{bmatrix}169&120\\104&173\end{bmatrix}$, $\begin{bmatrix}183&160\\145&157\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.144.7.fug.2 for the level structure with $-I$) |
Cyclic 240-isogeny field degree: | $8$ |
Cyclic 240-torsion field degree: | $256$ |
Full 240-torsion field degree: | $1966080$ |
Rational points
This modular curve has 4 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 |
---|---|---|---|---|---|
80.144.3-40.bx.1.18 | $80$ | $2$ | $2$ | $3$ | $?$ |
240.144.3-40.bx.1.15 | $240$ | $2$ | $2$ | $3$ | $?$ |