Invariants
Level: | $120$ | $\SL_2$-level: | $10$ | Newform level: | $1$ | ||
Index: | $40$ | $\PSL_2$-index: | $40$ | ||||
Genus: | $1 = 1 + \frac{ 40 }{12} - \frac{ 0 }{4} - \frac{ 4 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (none of which are rational) | Cusp widths | $10^{4}$ | Cusp orbits | $4$ | ||
Elliptic points: | $0$ of order $2$ and $4$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 40$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 10H1 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}1&109\\1&20\end{bmatrix}$, $\begin{bmatrix}53&39\\52&97\end{bmatrix}$, $\begin{bmatrix}79&78\\112&37\end{bmatrix}$, $\begin{bmatrix}81&113\\2&29\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | none in database |
Cyclic 120-isogeny field degree: | $288$ |
Cyclic 120-torsion field degree: | $9216$ |
Full 120-torsion field degree: | $884736$ |
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
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
30.20.1.a.1 | $30$ | $2$ | $2$ | $1$ | $1$ | dimension zero |
40.20.0.d.1 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.20.0.e.1 | $120$ | $2$ | $2$ | $0$ | $?$ | 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 |
---|---|---|---|---|---|---|
120.120.5.dj.1 | $120$ | $3$ | $3$ | $5$ | $?$ | not computed |
120.120.5.et.1 | $120$ | $3$ | $3$ | $5$ | $?$ | not computed |
120.120.7.hh.1 | $120$ | $3$ | $3$ | $7$ | $?$ | not computed |
120.120.9.nv.1 | $120$ | $3$ | $3$ | $9$ | $?$ | not computed |
120.160.9.dv.1 | $120$ | $4$ | $4$ | $9$ | $?$ | not computed |
120.160.9.eh.1 | $120$ | $4$ | $4$ | $9$ | $?$ | not computed |