Invariants
| Level: | $120$ | $\SL_2$-level: | $24$ | 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 | $2^{2}\cdot4^{2}\cdot6^{2}\cdot12^{2}$ | 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: | 12P1 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}1&5\\16&21\end{bmatrix}$, $\begin{bmatrix}15&67\\28&87\end{bmatrix}$, $\begin{bmatrix}27&58\\116&91\end{bmatrix}$, $\begin{bmatrix}29&48\\44&25\end{bmatrix}$, $\begin{bmatrix}41&25\\98&9\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.48.1.yw.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $24$ |
| 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 no real points, and therefore no rational points.
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| $X_0(3)$ | $3$ | $24$ | $12$ | $0$ | $0$ | full Jacobian |
| 40.24.0-40.m.1.4 | $40$ | $4$ | $4$ | $0$ | $0$ | full Jacobian |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 24.48.0-12.f.1.5 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 40.24.0-40.m.1.4 | $40$ | $4$ | $4$ | $0$ | $0$ | full Jacobian |
| 120.48.0-12.f.1.9 | $120$ | $2$ | $2$ | $0$ | $?$ | 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 |
|---|---|---|---|---|---|---|
| 120.192.3-120.mt.1.15 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.mt.1.16 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.mt.2.14 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.mt.2.16 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.mv.1.14 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.mv.1.16 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.mv.2.12 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.mv.2.16 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.qp.1.14 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.qp.1.16 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.qp.2.12 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.qp.2.16 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.qr.1.12 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.qr.1.16 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.qr.2.8 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.qr.2.16 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.288.5-120.zw.1.16 | $120$ | $3$ | $3$ | $5$ | $?$ | not computed |
| 120.480.17-120.bqc.1.24 | $120$ | $5$ | $5$ | $17$ | $?$ | not computed |