Invariants
Level: | $120$ | $\SL_2$-level: | $8$ | ||||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (of which $2$ are rational) | Cusp widths | $4^{8}\cdot8^{2}$ | Cusp orbits | $1^{2}\cdot2^{2}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $1$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8N0 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}33&76\\88&57\end{bmatrix}$, $\begin{bmatrix}47&56\\70&11\end{bmatrix}$, $\begin{bmatrix}57&76\\106&91\end{bmatrix}$, $\begin{bmatrix}113&92\\86&45\end{bmatrix}$, $\begin{bmatrix}119&16\\26&17\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.48.0.bm.2 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $48$ |
Cyclic 120-torsion field degree: | $1536$ |
Full 120-torsion field degree: | $368640$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
24.48.0-8.e.1.2 | $24$ | $2$ | $2$ | $0$ | $0$ |
40.48.0-8.e.1.5 | $40$ | $2$ | $2$ | $0$ | $0$ |
120.48.0-120.e.1.12 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.48.0-120.e.1.32 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.48.0-120.t.1.22 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.48.0-120.t.1.52 | $120$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
120.192.1-120.bf.1.10 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.db.1.6 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.eo.1.8 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.ew.1.12 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.ij.1.2 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.ir.1.12 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.ke.1.16 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.km.1.4 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.mf.1.2 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.mn.1.12 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.oa.1.16 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.oi.1.4 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.ph.1.10 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.pp.1.6 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.qb.1.8 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.qf.1.12 | $120$ | $2$ | $2$ | $1$ |
120.288.8-120.ed.2.48 | $120$ | $3$ | $3$ | $8$ |
120.384.7-120.dr.1.17 | $120$ | $4$ | $4$ | $7$ |
120.480.16-120.cb.2.15 | $120$ | $5$ | $5$ | $16$ |