Invariants
Level: | $120$ | $\SL_2$-level: | $8$ | ||||
Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
Cusps: | $6$ (none of which are rational) | Cusp widths | $2^{4}\cdot8^{2}$ | Cusp orbits | $2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8G0 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}29&96\\64&89\end{bmatrix}$, $\begin{bmatrix}35&4\\23&89\end{bmatrix}$, $\begin{bmatrix}57&20\\47&43\end{bmatrix}$, $\begin{bmatrix}91&100\\12&1\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 24.24.0.bo.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $48$ |
Cyclic 120-torsion field degree: | $1536$ |
Full 120-torsion field degree: | $737280$ |
Models
Smooth plane model Smooth plane model
$ 0 $ | $=$ | $ 3 x^{2} + 3 y^{2} + 16 z^{2} $ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
40.24.0-8.o.1.2 | $40$ | $2$ | $2$ | $0$ | $0$ |
120.24.0-12.g.1.2 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.24.0-12.g.1.4 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.24.0-8.o.1.8 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.24.0-24.z.1.8 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.24.0-24.z.1.13 | $120$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
120.144.4-24.fo.1.1 | $120$ | $3$ | $3$ | $4$ |
120.192.3-24.fs.1.9 | $120$ | $4$ | $4$ | $3$ |
120.240.8-120.dq.1.3 | $120$ | $5$ | $5$ | $8$ |
120.288.7-120.dlj.1.11 | $120$ | $6$ | $6$ | $7$ |
120.480.15-120.ja.1.6 | $120$ | $10$ | $10$ | $15$ |
240.96.1-48.y.1.7 | $240$ | $2$ | $2$ | $1$ |
240.96.1-48.ba.1.8 | $240$ | $2$ | $2$ | $1$ |
240.96.1-240.by.1.15 | $240$ | $2$ | $2$ | $1$ |
240.96.1-240.bz.1.16 | $240$ | $2$ | $2$ | $1$ |
240.96.1-48.cm.1.6 | $240$ | $2$ | $2$ | $1$ |
240.96.1-48.co.1.3 | $240$ | $2$ | $2$ | $1$ |
240.96.1-240.du.1.7 | $240$ | $2$ | $2$ | $1$ |
240.96.1-240.dv.1.5 | $240$ | $2$ | $2$ | $1$ |