Invariants
Level: | $120$ | $\SL_2$-level: | $40$ | 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: | 40M7 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}19&100\\51&11\end{bmatrix}$, $\begin{bmatrix}41&100\\14&99\end{bmatrix}$, $\begin{bmatrix}49&80\\12&109\end{bmatrix}$, $\begin{bmatrix}53&20\\116&91\end{bmatrix}$, $\begin{bmatrix}83&40\\55&57\end{bmatrix}$, $\begin{bmatrix}101&60\\62&59\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.144.7.dkm.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
The following modular covers realize this modular curve as a fiber product over $X(1)$.
Factor curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
$X_0(5)$ | $5$ | $48$ | $24$ | $0$ | $0$ |
24.48.0-24.bh.1.1 | $24$ | $6$ | $6$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
24.48.0-24.bh.1.1 | $24$ | $6$ | $6$ | $0$ | $0$ |
40.144.3-40.bx.1.38 | $40$ | $2$ | $2$ | $3$ | $0$ |
60.144.3-60.es.1.7 | $60$ | $2$ | $2$ | $3$ | $1$ |
120.144.3-40.bx.1.29 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.144.3-60.es.1.18 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.144.3-120.byo.1.8 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.144.3-120.byo.1.41 | $120$ | $2$ | $2$ | $3$ | $?$ |