Invariants
Level: | $120$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $4^{4}\cdot8^{4}$ | Cusp orbits | $2^{2}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 48$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8F1 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}7&72\\99&101\end{bmatrix}$, $\begin{bmatrix}35&28\\12&67\end{bmatrix}$, $\begin{bmatrix}41&56\\94&41\end{bmatrix}$, $\begin{bmatrix}77&32\\83&27\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.48.1.ms.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $48$ |
Cyclic 120-torsion field degree: | $1536$ |
Full 120-torsion field degree: | $368640$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
40.48.0-20.d.1.5 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
60.48.0-20.d.1.1 | $60$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
24.48.1-24.n.1.4 | $24$ | $2$ | $2$ | $1$ | $1$ | dimension zero |
120.48.1-24.n.1.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.48.0-120.br.1.3 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.48.0-120.br.1.12 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
120.288.9-120.dww.1.7 | $120$ | $3$ | $3$ | $9$ | $?$ | not computed |
120.384.9-120.bie.1.3 | $120$ | $4$ | $4$ | $9$ | $?$ | not computed |
120.480.17-120.ty.1.2 | $120$ | $5$ | $5$ | $17$ | $?$ | not computed |