Invariants
| Level: | $120$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (of which $4$ are rational) | Cusp widths | $8^{12}$ | Cusp orbits | $1^{4}\cdot2^{2}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 3$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 8B3 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}9&8\\68&35\end{bmatrix}$, $\begin{bmatrix}17&112\\88&27\end{bmatrix}$, $\begin{bmatrix}33&92\\44&87\end{bmatrix}$, $\begin{bmatrix}81&40\\40&53\end{bmatrix}$, $\begin{bmatrix}105&116\\68&83\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.96.3.cw.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $48$ |
| Cyclic 120-torsion field degree: | $384$ |
| Full 120-torsion field degree: | $184320$ |
Rational points
This modular curve has 4 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.96.0-8.c.1.1 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 120.96.0-8.c.1.4 | $120$ | $2$ | $2$ | $0$ | $?$ |
| 120.96.1-120.n.1.1 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.96.1-120.n.1.13 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.96.2-120.a.1.11 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.96.2-120.a.1.47 | $120$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.384.5-120.hp.1.2 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.hp.2.3 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.hq.1.3 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.hq.2.5 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.hu.1.1 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.hu.2.1 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.hv.2.1 | $120$ | $2$ | $2$ | $5$ |
| 120.384.5-120.hv.3.1 | $120$ | $2$ | $2$ | $5$ |
| 240.384.7-240.m.1.26 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.p.1.2 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.q.1.18 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.t.1.2 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.cg.1.2 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.ch.1.2 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.co.1.1 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.cp.1.3 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.fm.1.3 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.fn.1.3 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.fu.1.2 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.fv.1.1 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.hi.1.2 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.hl.1.2 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.hm.1.2 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.hp.1.1 | $240$ | $2$ | $2$ | $7$ |