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 | $2^{4}$ | ||
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: | $\begin{bmatrix}9&104\\52&53\end{bmatrix}$, $\begin{bmatrix}35&76\\16&109\end{bmatrix}$, $\begin{bmatrix}55&84\\62&23\end{bmatrix}$, $\begin{bmatrix}83&28\\12&55\end{bmatrix}$, $\begin{bmatrix}107&68\\106&23\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.48.1.fc.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $48$ |
Cyclic 120-torsion field degree: | $768$ |
Full 120-torsion field degree: | $368640$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
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
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
24.48.0-24.m.1.1 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
40.48.0-20.c.1.15 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
60.48.0-20.c.1.1 | $60$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.48.0-24.m.1.19 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.48.1-120.c.1.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.48.1-120.c.1.31 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
120.192.1-120.ne.1.10 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ne.2.2 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ng.1.10 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ng.2.2 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ni.1.9 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ni.2.4 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.nk.1.12 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.nk.2.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.nm.1.16 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.nm.2.9 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.no.1.13 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.no.2.12 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.nq.1.14 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.nq.2.10 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ns.1.14 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ns.2.10 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.288.9-120.bay.1.62 | $120$ | $3$ | $3$ | $9$ | $?$ | not computed |
120.384.9-120.nu.1.8 | $120$ | $4$ | $4$ | $9$ | $?$ | not computed |
120.480.17-120.hk.1.4 | $120$ | $5$ | $5$ | $17$ | $?$ | not computed |