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 | $1^{2}\cdot2\cdot8$ | 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: | 8C0 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}3&112\\22&109\end{bmatrix}$, $\begin{bmatrix}5&84\\94&119\end{bmatrix}$, $\begin{bmatrix}12&67\\101&18\end{bmatrix}$, $\begin{bmatrix}39&14\\38&107\end{bmatrix}$, $\begin{bmatrix}64&85\\55&54\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.12.0.bb.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $48$ |
Cyclic 120-torsion field degree: | $1536$ |
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.1.3 | $8$ | $2$ | $2$ | $0$ | $0$ |
120.12.0-4.c.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 |
---|---|---|---|---|
120.48.0-120.x.1.23 | $120$ | $2$ | $2$ | $0$ |
120.48.0-120.ba.1.8 | $120$ | $2$ | $2$ | $0$ |
120.48.0-120.br.1.2 | $120$ | $2$ | $2$ | $0$ |
120.48.0-120.bs.1.2 | $120$ | $2$ | $2$ | $0$ |
120.48.0-120.bu.1.13 | $120$ | $2$ | $2$ | $0$ |
120.48.0-120.bx.1.7 | $120$ | $2$ | $2$ | $0$ |
120.48.0-120.ch.1.6 | $120$ | $2$ | $2$ | $0$ |
120.48.0-120.ci.1.3 | $120$ | $2$ | $2$ | $0$ |
120.48.0-120.cm.1.13 | $120$ | $2$ | $2$ | $0$ |
120.48.0-120.cp.1.6 | $120$ | $2$ | $2$ | $0$ |
120.48.0-120.cz.1.13 | $120$ | $2$ | $2$ | $0$ |
120.48.0-120.da.1.2 | $120$ | $2$ | $2$ | $0$ |
120.48.0-120.dc.1.9 | $120$ | $2$ | $2$ | $0$ |
120.48.0-120.df.1.5 | $120$ | $2$ | $2$ | $0$ |
120.48.0-120.ef.1.5 | $120$ | $2$ | $2$ | $0$ |
120.48.0-120.eg.1.1 | $120$ | $2$ | $2$ | $0$ |
120.72.2-120.dh.1.50 | $120$ | $3$ | $3$ | $2$ |
120.96.1-120.zz.1.42 | $120$ | $4$ | $4$ | $1$ |
120.120.4-120.cb.1.1 | $120$ | $5$ | $5$ | $4$ |
120.144.3-120.byn.1.38 | $120$ | $6$ | $6$ | $3$ |
120.240.7-120.dh.1.40 | $120$ | $10$ | $10$ | $7$ |