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: | $\begin{bmatrix}5&46\\78&19\end{bmatrix}$, $\begin{bmatrix}19&66\\100&77\end{bmatrix}$, $\begin{bmatrix}75&86\\14&33\end{bmatrix}$, $\begin{bmatrix}107&96\\12&77\end{bmatrix}$, $\begin{bmatrix}118&113\\85&54\end{bmatrix}$ |
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.1.9 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.24.0-6.a.1.11 | $120$ | $2$ | $2$ | $0$ | $?$ | 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.1.11 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.gh.1.14 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.kc.1.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.kd.1.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.zi.1.14 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.zj.1.6 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.zr.1.22 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.zs.1.10 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.bac.1.7 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.bad.1.15 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.bal.1.13 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.bam.1.15 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.bao.1.14 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.bap.1.6 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.bax.1.7 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.bay.1.5 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.144.3-120.dae.1.9 | $120$ | $3$ | $3$ | $3$ | $?$ | not computed |
120.240.9-120.xh.1.30 | $120$ | $5$ | $5$ | $9$ | $?$ | not computed |
120.288.9-120.rvb.1.40 | $120$ | $6$ | $6$ | $9$ | $?$ | not computed |
120.480.17-120.gid.1.50 | $120$ | $10$ | $10$ | $17$ | $?$ | not computed |