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: | 12B2 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}7&51\\84&79\end{bmatrix}$, $\begin{bmatrix}17&23\\86&85\end{bmatrix}$, $\begin{bmatrix}47&79\\112&103\end{bmatrix}$, $\begin{bmatrix}91&98\\86&81\end{bmatrix}$, $\begin{bmatrix}119&53\\98&7\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.36.2.bw.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 no real points, and therefore no rational points.
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| $X_{\mathrm{ns}}^+(3)$ | $3$ | $24$ | $12$ | $0$ | $0$ |
| 40.24.0-40.m.1.4 | $40$ | $3$ | $3$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.36.1-12.b.1.9 | $24$ | $2$ | $2$ | $1$ | $0$ |
| 40.24.0-40.m.1.4 | $40$ | $3$ | $3$ | $0$ | $0$ |
| 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.bgz.1.8 | $120$ | $2$ | $2$ | $3$ |
| 120.144.3-120.bha.1.8 | $120$ | $2$ | $2$ | $3$ |
| 120.144.3-120.bhg.1.6 | $120$ | $2$ | $2$ | $3$ |
| 120.144.3-120.bhh.1.8 | $120$ | $2$ | $2$ | $3$ |
| 120.144.3-120.blh.1.12 | $120$ | $2$ | $2$ | $3$ |
| 120.144.3-120.bli.1.8 | $120$ | $2$ | $2$ | $3$ |
| 120.144.3-120.blo.1.8 | $120$ | $2$ | $2$ | $3$ |
| 120.144.3-120.blp.1.8 | $120$ | $2$ | $2$ | $3$ |
| 120.144.3-120.bpp.1.8 | $120$ | $2$ | $2$ | $3$ |
| 120.144.3-120.bpq.1.7 | $120$ | $2$ | $2$ | $3$ |
| 120.144.3-120.bpw.1.8 | $120$ | $2$ | $2$ | $3$ |
| 120.144.3-120.bpx.1.8 | $120$ | $2$ | $2$ | $3$ |
| 120.144.3-120.btx.1.8 | $120$ | $2$ | $2$ | $3$ |
| 120.144.3-120.bty.1.8 | $120$ | $2$ | $2$ | $3$ |
| 120.144.3-120.bue.1.8 | $120$ | $2$ | $2$ | $3$ |
| 120.144.3-120.buf.1.8 | $120$ | $2$ | $2$ | $3$ |
| 120.360.14-120.ee.1.14 | $120$ | $5$ | $5$ | $14$ |
| 120.432.15-120.ga.1.32 | $120$ | $6$ | $6$ | $15$ |