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: | $\begin{bmatrix}46&33\\37&92\end{bmatrix}$, $\begin{bmatrix}69&4\\88&15\end{bmatrix}$, $\begin{bmatrix}99&94\\104&37\end{bmatrix}$, $\begin{bmatrix}109&86\\90&53\end{bmatrix}$, $\begin{bmatrix}117&16\\86&31\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.24.1.iw.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.1.7 | $120$ | $2$ | $2$ | $0$ | $?$ | 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 |
---|---|---|---|---|---|---|
120.96.1-120.dh.1.19 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.gg.1.10 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.jw.1.11 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.jx.1.5 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.yz.1.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.za.1.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.zc.1.6 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.zd.1.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.bkw.1.2 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.bkx.1.2 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.blc.1.2 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.bld.1.2 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.bli.1.9 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.blj.1.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.blo.1.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.blp.1.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.144.3-120.dnu.1.3 | $120$ | $3$ | $3$ | $3$ | $?$ | not computed |
120.240.9-120.xi.1.5 | $120$ | $5$ | $5$ | $9$ | $?$ | not computed |
120.288.9-120.rvc.1.13 | $120$ | $6$ | $6$ | $9$ | $?$ | not computed |
120.480.17-120.gie.1.51 | $120$ | $10$ | $10$ | $17$ | $?$ | not computed |