Invariants
| Level: | $120$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
| Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (all of which are rational) | Cusp widths | $2\cdot4\cdot6\cdot12$ | Cusp orbits | $1^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 12F1 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}3&64\\2&103\end{bmatrix}$, $\begin{bmatrix}35&112\\6&13\end{bmatrix}$, $\begin{bmatrix}50&111\\47&58\end{bmatrix}$, $\begin{bmatrix}57&100\\14&19\end{bmatrix}$, $\begin{bmatrix}78&79\\41&52\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.24.1.iv.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $24$ |
| Cyclic 120-torsion field degree: | $768$ |
| Full 120-torsion field degree: | $737280$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | not computed |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 12.24.0-6.a.1.6 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 120.24.0-6.a.1.6 | $120$ | $2$ | $2$ | $0$ | $?$ | 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 |
|---|---|---|---|---|---|---|
| 120.96.1-120.di.1.9 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.gh.1.2 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.kc.1.13 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.kd.1.6 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.zi.1.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.zj.1.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.zr.1.6 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.zs.1.5 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.bac.1.4 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.bad.1.5 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.bal.1.7 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.bam.1.6 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.bao.1.9 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.bap.1.7 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.bax.1.6 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.bay.1.7 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.144.3-120.dae.1.7 | $120$ | $3$ | $3$ | $3$ | $?$ | not computed |
| 120.240.9-120.xh.1.9 | $120$ | $5$ | $5$ | $9$ | $?$ | not computed |
| 120.288.9-120.rvb.1.21 | $120$ | $6$ | $6$ | $9$ | $?$ | not computed |
| 120.480.17-120.gid.1.25 | $120$ | $10$ | $10$ | $17$ | $?$ | not computed |