Invariants
Level: | $120$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
Index: | $480$ | $\PSL_2$-index: | $240$ | ||||
Genus: | $15 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $10^{8}\cdot40^{4}$ | Cusp orbits | $2^{2}\cdot4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $4 \le \gamma \le 28$ | ||||||
$\overline{\Q}$-gonality: | $4 \le \gamma \le 15$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 40C15 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}13&104\\44&51\end{bmatrix}$, $\begin{bmatrix}31&36\\56&49\end{bmatrix}$, $\begin{bmatrix}35&106\\76&27\end{bmatrix}$, $\begin{bmatrix}77&22\\52&51\end{bmatrix}$, $\begin{bmatrix}93&110\\40&113\end{bmatrix}$, $\begin{bmatrix}109&98\\40&21\end{bmatrix}$, $\begin{bmatrix}119&36\\52&31\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.240.15.et.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $48$ |
Cyclic 120-torsion field degree: | $768$ |
Full 120-torsion field degree: | $73728$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
Factor curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
$X_{\mathrm{ns}}^+(5)$ | $5$ | $48$ | $24$ | $0$ | $0$ |
24.48.0-24.m.1.5 | $24$ | $10$ | $10$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
24.48.0-24.m.1.5 | $24$ | $10$ | $10$ | $0$ | $0$ |
40.240.7-20.b.1.44 | $40$ | $2$ | $2$ | $7$ | $0$ |
60.240.7-20.b.1.3 | $60$ | $2$ | $2$ | $7$ | $0$ |
120.240.7-120.cv.1.17 | $120$ | $2$ | $2$ | $7$ | $?$ |
120.240.7-120.cv.1.48 | $120$ | $2$ | $2$ | $7$ | $?$ |
120.240.7-120.di.1.17 | $120$ | $2$ | $2$ | $7$ | $?$ |
120.240.7-120.di.1.48 | $120$ | $2$ | $2$ | $7$ | $?$ |