Invariants
| Level: | $120$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $2 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (none of which are rational) | Cusp widths | $8^{6}$ | Cusp orbits | $2^{3}$ | ||
| 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: | 8A2 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}7&88\\90&31\end{bmatrix}$, $\begin{bmatrix}15&94\\62&57\end{bmatrix}$, $\begin{bmatrix}23&92\\104&63\end{bmatrix}$, $\begin{bmatrix}85&84\\16&97\end{bmatrix}$, $\begin{bmatrix}107&66\\78&73\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.48.2.c.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $96$ |
| Cyclic 120-torsion field degree: | $3072$ |
| Full 120-torsion field degree: | $368640$ |
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 |
|---|---|---|---|---|---|
| 40.48.0-20.b.1.9 | $40$ | $2$ | $2$ | $0$ | $0$ |
| 120.48.0-20.b.1.3 | $120$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.192.3-120.h.1.3 | $120$ | $2$ | $2$ | $3$ |
| 120.192.3-120.j.1.2 | $120$ | $2$ | $2$ | $3$ |
| 120.192.3-120.l.1.1 | $120$ | $2$ | $2$ | $3$ |
| 120.192.3-120.n.1.1 | $120$ | $2$ | $2$ | $3$ |
| 120.192.3-120.cy.1.6 | $120$ | $2$ | $2$ | $3$ |
| 120.192.3-120.de.1.6 | $120$ | $2$ | $2$ | $3$ |
| 120.192.3-120.dg.1.2 | $120$ | $2$ | $2$ | $3$ |
| 120.192.3-120.dm.1.2 | $120$ | $2$ | $2$ | $3$ |
| 120.192.3-120.gq.1.1 | $120$ | $2$ | $2$ | $3$ |
| 120.192.3-120.gw.1.1 | $120$ | $2$ | $2$ | $3$ |
| 120.192.3-120.gy.1.5 | $120$ | $2$ | $2$ | $3$ |
| 120.192.3-120.he.1.3 | $120$ | $2$ | $2$ | $3$ |
| 120.192.3-120.hg.1.2 | $120$ | $2$ | $2$ | $3$ |
| 120.192.3-120.hi.1.2 | $120$ | $2$ | $2$ | $3$ |
| 120.192.3-120.hk.1.4 | $120$ | $2$ | $2$ | $3$ |
| 120.192.3-120.hm.1.4 | $120$ | $2$ | $2$ | $3$ |
| 120.288.10-120.f.1.32 | $120$ | $3$ | $3$ | $10$ |
| 120.384.11-120.f.1.12 | $120$ | $4$ | $4$ | $11$ |
| 120.480.18-120.e.1.23 | $120$ | $5$ | $5$ | $18$ |