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 | $1^{2}\cdot2^{3}\cdot5^{2}\cdot10^{3}\cdot16\cdot80$ | 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: | 80G7 |
Level structure
$\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}12&191\\119&204\end{bmatrix}$, $\begin{bmatrix}13&78\\2&49\end{bmatrix}$, $\begin{bmatrix}76&217\\17&196\end{bmatrix}$, $\begin{bmatrix}84&13\\161&96\end{bmatrix}$, $\begin{bmatrix}107&166\\166&27\end{bmatrix}$, $\begin{bmatrix}116&51\\193&94\end{bmatrix}$, $\begin{bmatrix}118&83\\99&182\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.144.7.ul.4 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 | $80$ | $2$ | $2$ | $3$ | $?$ |
120.144.3-40.bx.1.9 | $120$ | $2$ | $2$ | $3$ | $?$ |