Invariants
| Level: | $120$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
| Index: | $24$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (none of which are rational) | Cusp widths | $4^{2}\cdot8^{2}$ | Cusp orbits | $2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 24$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 8C1 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}35&22\\18&103\end{bmatrix}$, $\begin{bmatrix}57&116\\68&95\end{bmatrix}$, $\begin{bmatrix}68&67\\69&40\end{bmatrix}$, $\begin{bmatrix}75&92\\44&75\end{bmatrix}$, $\begin{bmatrix}88&107\\15&52\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 120-isogeny field degree: | $96$ |
| Cyclic 120-torsion field degree: | $3072$ |
| Full 120-torsion field degree: | $1474560$ |
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 |
|---|---|---|---|---|---|---|
| 8.12.0.q.1 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 60.12.0.bn.1 | $60$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 120.12.1.dy.1 | $120$ | $2$ | $2$ | $1$ | $?$ | 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 |
|---|---|---|---|---|---|---|
| 120.48.1.fl.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.48.1.gw.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.48.1.iv.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.48.1.ja.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.48.1.blz.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.48.1.bmd.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.48.1.bmo.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.48.1.bms.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.48.1.cap.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.48.1.cat.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.48.1.cbe.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.48.1.cbi.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.48.1.cnf.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.48.1.cnj.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.48.1.cnu.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.48.1.cny.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.72.5.btd.1 | $120$ | $3$ | $3$ | $5$ | $?$ | not computed |
| 120.96.5.rp.1 | $120$ | $4$ | $4$ | $5$ | $?$ | not computed |
| 120.120.9.yv.1 | $120$ | $5$ | $5$ | $9$ | $?$ | not computed |
| 120.144.9.stz.1 | $120$ | $6$ | $6$ | $9$ | $?$ | not computed |
| 120.240.17.hjn.1 | $120$ | $10$ | $10$ | $17$ | $?$ | not computed |