Invariants
Level: | $120$ | $\SL_2$-level: | $24$ | 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: | $12$ (none of which are rational) | Cusp widths | $6^{8}\cdot24^{4}$ | Cusp orbits | $4^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 12$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 7$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24J7 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}9&112\\88&35\end{bmatrix}$, $\begin{bmatrix}39&11\\8&91\end{bmatrix}$, $\begin{bmatrix}63&112\\52&95\end{bmatrix}$, $\begin{bmatrix}71&77\\56&9\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.144.7.bnn.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $48$ |
Cyclic 120-torsion field degree: | $1536$ |
Full 120-torsion field degree: | $122880$ |
Rational points
This modular curve has no real points and no $\Q_p$ points for $p=7$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
24.144.3-24.ca.1.6 | $24$ | $2$ | $2$ | $3$ | $1$ |
120.144.3-24.ca.1.2 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.144.3-120.byv.1.3 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.144.3-120.byv.1.22 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.144.3-120.bzh.1.3 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.144.3-120.bzh.1.14 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.144.4-120.ex.1.3 | $120$ | $2$ | $2$ | $4$ | $?$ |
120.144.4-120.ex.1.10 | $120$ | $2$ | $2$ | $4$ | $?$ |
120.144.4-120.fa.1.9 | $120$ | $2$ | $2$ | $4$ | $?$ |
120.144.4-120.fa.1.32 | $120$ | $2$ | $2$ | $4$ | $?$ |
120.144.4-120.vl.1.18 | $120$ | $2$ | $2$ | $4$ | $?$ |
120.144.4-120.vl.1.29 | $120$ | $2$ | $2$ | $4$ | $?$ |
120.144.4-120.vx.1.2 | $120$ | $2$ | $2$ | $4$ | $?$ |
120.144.4-120.vx.1.13 | $120$ | $2$ | $2$ | $4$ | $?$ |