Invariants
| Level: | $120$ | $\SL_2$-level: | $12$ | 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: | $8$ (of which $4$ are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot6^{2}\cdot12^{2}$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
| 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: | 12P1 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}21&4\\8&43\end{bmatrix}$, $\begin{bmatrix}33&14\\2&45\end{bmatrix}$, $\begin{bmatrix}33&88\\112&3\end{bmatrix}$, $\begin{bmatrix}37&78\\24&13\end{bmatrix}$, $\begin{bmatrix}113&52\\0&103\end{bmatrix}$, $\begin{bmatrix}113&100\\86&27\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.48.1.dg.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $24$ |
| Cyclic 120-torsion field degree: | $384$ |
| Full 120-torsion field degree: | $368640$ |
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
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.a.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 |
|---|---|---|---|---|---|---|
| 12.48.0-6.a.1.1 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 40.24.0-40.a.1.4 | $40$ | $4$ | $4$ | $0$ | $0$ | full Jacobian |
| 120.48.0-6.a.1.7 | $120$ | $2$ | $2$ | $0$ | $?$ | 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 |
|---|---|---|---|---|---|---|
| 120.192.1-120.lm.1.12 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.lm.1.16 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.lm.2.9 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.lm.2.13 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.lm.3.8 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.lm.3.16 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.lm.4.5 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.lm.4.13 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.lo.1.11 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.lo.1.15 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.lo.2.11 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.lo.2.15 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.lo.3.7 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.lo.3.15 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.lo.4.7 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.lo.4.15 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.3-120.do.1.1 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.do.1.2 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.dp.1.1 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.dp.1.2 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.ds.1.2 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.ds.1.59 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.du.1.10 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.du.1.28 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.ec.1.1 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.ec.1.2 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.ee.1.29 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.ee.1.30 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.ei.1.9 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.ei.1.26 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.ek.1.2 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.ek.1.20 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.fk.1.1 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.fk.1.3 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.fk.2.1 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.fk.2.3 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.fm.1.1 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.fm.1.2 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.fm.2.1 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.fm.2.2 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.gf.1.1 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.gf.1.3 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.gf.2.1 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.gf.2.3 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.gg.1.1 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.gg.1.2 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.gg.2.1 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.gg.2.2 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.288.5-120.a.1.16 | $120$ | $3$ | $3$ | $5$ | $?$ | not computed |
| 120.480.17-120.fk.1.1 | $120$ | $5$ | $5$ | $17$ | $?$ | not computed |