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: | $8$ (of which $4$ are rational) | Cusp widths | $1^{2}\cdot2\cdot3^{2}\cdot6\cdot8\cdot24$ | 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: | 24G1 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}31&56\\6&29\end{bmatrix}$, $\begin{bmatrix}35&114\\116&49\end{bmatrix}$, $\begin{bmatrix}41&100\\26&39\end{bmatrix}$, $\begin{bmatrix}44&27\\95&28\end{bmatrix}$, $\begin{bmatrix}56&73\\83&18\end{bmatrix}$, $\begin{bmatrix}62&57\\35&88\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.48.1.zu.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $12$ |
| 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 |
|---|---|---|---|---|---|---|
| 3.8.0-3.a.1.1 | $3$ | $12$ | $12$ | $0$ | $0$ | full Jacobian |
| 40.12.0.y.1 | $40$ | $8$ | $4$ | $0$ | $0$ | full Jacobian |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 12.48.0-12.g.1.10 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 120.48.0-12.g.1.22 | $120$ | $2$ | $2$ | $0$ | $?$ | 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.rb.1.6 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.rb.2.6 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.rb.3.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.rb.4.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.rd.1.12 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.rd.2.12 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.rd.3.6 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.rd.4.6 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.sl.1.8 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.sl.2.8 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.sl.3.7 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.sl.4.7 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.sn.1.16 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.sn.2.16 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.sn.3.14 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.sn.4.14 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.3-120.gc.1.78 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.hq.1.32 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.jg.1.40 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.ji.1.32 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.lu.1.31 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.lw.1.31 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.mg.1.31 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.mi.1.31 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.oc.1.32 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.of.1.48 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.ox.1.31 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.oy.1.32 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.pq.1.32 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.pt.1.32 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.pz.1.32 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.qa.1.32 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.si.1.25 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.si.2.27 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.si.3.21 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.si.4.27 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.sk.1.29 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.sk.2.30 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.sk.3.27 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.sk.4.30 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.tg.1.27 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.tg.2.31 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.tg.3.23 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.tg.4.31 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.ti.1.30 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.ti.2.32 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.ti.3.28 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.ti.4.32 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.288.5-120.bee.1.1 | $120$ | $3$ | $3$ | $5$ | $?$ | not computed |
| 120.480.17-120.bre.1.62 | $120$ | $5$ | $5$ | $17$ | $?$ | not computed |