Invariants
Level: | $120$ | $\SL_2$-level: | $60$ | 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 | $2^{3}\cdot6^{3}\cdot10^{3}\cdot30^{3}$ | 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: | 30S7 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}51&16\\50&19\end{bmatrix}$, $\begin{bmatrix}69&17\\20&93\end{bmatrix}$, $\begin{bmatrix}91&26\\90&101\end{bmatrix}$, $\begin{bmatrix}99&13\\80&103\end{bmatrix}$, $\begin{bmatrix}103&45\\0&109\end{bmatrix}$, $\begin{bmatrix}109&74\\100&63\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.144.7.hna.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $4$ |
Cyclic 120-torsion field degree: | $128$ |
Full 120-torsion field degree: | $122880$ |
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 |
---|---|---|---|---|---|
60.144.3-30.a.1.9 | $60$ | $2$ | $2$ | $3$ | $0$ |
120.144.3-30.a.1.36 | $120$ | $2$ | $2$ | $3$ | $?$ |