Invariants
Level: | $120$ | $\SL_2$-level: | $8$ | ||||
Index: | $24$ | $\PSL_2$-index: | $12$ | ||||
Genus: | $0 = 1 + \frac{ 12 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (of which $2$ are rational) | Cusp widths | $2^{2}\cdot4^{2}$ | Cusp orbits | $1^{2}\cdot2$ | ||
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: | 4E0 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}17&80\\15&77\end{bmatrix}$, $\begin{bmatrix}25&48\\66&79\end{bmatrix}$, $\begin{bmatrix}33&88\\43&41\end{bmatrix}$, $\begin{bmatrix}35&76\\8&111\end{bmatrix}$, $\begin{bmatrix}41&40\\113&59\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.12.0.s.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $48$ |
Cyclic 120-torsion field degree: | $768$ |
Full 120-torsion field degree: | $1474560$ |
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 |
---|---|---|---|---|---|
8.12.0-4.c.1.5 | $8$ | $2$ | $2$ | $0$ | $0$ |
120.12.0-4.c.1.6 | $120$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
120.48.0-120.de.1.3 | $120$ | $2$ | $2$ | $0$ |
120.48.0-120.de.1.7 | $120$ | $2$ | $2$ | $0$ |
120.48.0-120.df.1.9 | $120$ | $2$ | $2$ | $0$ |
120.48.0-120.df.1.13 | $120$ | $2$ | $2$ | $0$ |
120.48.0-120.dq.1.5 | $120$ | $2$ | $2$ | $0$ |
120.48.0-120.dq.1.13 | $120$ | $2$ | $2$ | $0$ |
120.48.0-120.dr.1.5 | $120$ | $2$ | $2$ | $0$ |
120.48.0-120.dr.1.7 | $120$ | $2$ | $2$ | $0$ |
120.48.0-120.du.1.3 | $120$ | $2$ | $2$ | $0$ |
120.48.0-120.du.1.7 | $120$ | $2$ | $2$ | $0$ |
120.48.0-120.dv.1.9 | $120$ | $2$ | $2$ | $0$ |
120.48.0-120.dv.1.13 | $120$ | $2$ | $2$ | $0$ |
120.48.0-120.dy.1.5 | $120$ | $2$ | $2$ | $0$ |
120.48.0-120.dy.1.13 | $120$ | $2$ | $2$ | $0$ |
120.48.0-120.dz.1.5 | $120$ | $2$ | $2$ | $0$ |
120.48.0-120.dz.1.7 | $120$ | $2$ | $2$ | $0$ |
120.72.2-120.co.1.23 | $120$ | $3$ | $3$ | $2$ |
120.96.1-120.zo.1.32 | $120$ | $4$ | $4$ | $1$ |
120.120.4-120.bq.1.10 | $120$ | $5$ | $5$ | $4$ |
120.144.3-120.bgs.1.22 | $120$ | $6$ | $6$ | $3$ |
120.240.7-120.co.1.23 | $120$ | $10$ | $10$ | $7$ |