Invariants
| Level: | $120$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $72$ | $\PSL_2$-index: | $36$ | ||||
| Genus: | $2 = 1 + \frac{ 36 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (none of which are rational) | Cusp widths | $6^{2}\cdot12^{2}$ | Cusp orbits | $2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 12D2 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}19&36\\52&11\end{bmatrix}$, $\begin{bmatrix}58&117\\99&100\end{bmatrix}$, $\begin{bmatrix}106&105\\45&52\end{bmatrix}$, $\begin{bmatrix}118&23\\89&0\end{bmatrix}$, $\begin{bmatrix}118&95\\119&48\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.36.2.dz.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $96$ |
| Cyclic 120-torsion field degree: | $3072$ |
| Full 120-torsion field degree: | $491520$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.36.1-12.b.1.15 | $24$ | $2$ | $2$ | $1$ | $0$ |
| 120.36.1-12.b.1.16 | $120$ | $2$ | $2$ | $1$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.144.3-120.bc.1.25 | $120$ | $2$ | $2$ | $3$ |
| 120.144.3-120.fw.1.6 | $120$ | $2$ | $2$ | $3$ |
| 120.144.3-120.or.1.16 | $120$ | $2$ | $2$ | $3$ |
| 120.144.3-120.ou.1.6 | $120$ | $2$ | $2$ | $3$ |
| 120.144.3-120.bep.1.5 | $120$ | $2$ | $2$ | $3$ |
| 120.144.3-120.beq.1.6 | $120$ | $2$ | $2$ | $3$ |
| 120.144.3-120.bfd.1.5 | $120$ | $2$ | $2$ | $3$ |
| 120.144.3-120.bfe.1.4 | $120$ | $2$ | $2$ | $3$ |
| 120.144.3-120.bgy.1.5 | $120$ | $2$ | $2$ | $3$ |
| 120.144.3-120.bgz.1.8 | $120$ | $2$ | $2$ | $3$ |
| 120.144.3-120.bht.1.6 | $120$ | $2$ | $2$ | $3$ |
| 120.144.3-120.bhu.1.8 | $120$ | $2$ | $2$ | $3$ |
| 120.144.3-120.bnk.1.6 | $120$ | $2$ | $2$ | $3$ |
| 120.144.3-120.bnl.1.3 | $120$ | $2$ | $2$ | $3$ |
| 120.144.3-120.bof.1.6 | $120$ | $2$ | $2$ | $3$ |
| 120.144.3-120.bog.1.2 | $120$ | $2$ | $2$ | $3$ |
| 120.360.14-120.gx.1.11 | $120$ | $5$ | $5$ | $14$ |
| 120.432.15-120.kh.1.26 | $120$ | $6$ | $6$ | $15$ |