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: | $10$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{2}$ | Cusp orbits | $2^{3}\cdot4$ | ||
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: | 8N0 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}13&18\\80&53\end{bmatrix}$, $\begin{bmatrix}49&28\\44&51\end{bmatrix}$, $\begin{bmatrix}83&64\\92&47\end{bmatrix}$, $\begin{bmatrix}97&10\\88&119\end{bmatrix}$, $\begin{bmatrix}115&102\\52&107\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 24.48.0.l.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
Smooth plane model Smooth plane model
$ 0 $ | $=$ | $ 4 x^{2} - 4 x y + 7 y^{2} + 6 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 |
---|---|---|---|---|---|
40.48.0-8.d.2.8 | $40$ | $2$ | $2$ | $0$ | $0$ |
120.48.0-8.d.2.13 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.48.0-24.e.1.17 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.48.0-24.e.1.19 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.48.0-24.i.2.10 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.48.0-24.i.2.22 | $120$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
120.192.1-24.d.2.4 | $120$ | $2$ | $2$ | $1$ |
120.192.1-24.u.1.6 | $120$ | $2$ | $2$ | $1$ |
120.192.1-24.bi.1.7 | $120$ | $2$ | $2$ | $1$ |
120.192.1-24.bm.2.8 | $120$ | $2$ | $2$ | $1$ |
120.192.1-24.bt.1.4 | $120$ | $2$ | $2$ | $1$ |
120.192.1-24.bx.2.4 | $120$ | $2$ | $2$ | $1$ |
120.192.1-24.ce.2.6 | $120$ | $2$ | $2$ | $1$ |
120.192.1-24.cg.1.6 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.hb.2.5 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.hf.2.7 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.hr.2.15 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.hv.2.11 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.jn.2.2 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.jr.2.4 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.kd.2.12 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.kh.2.10 | $120$ | $2$ | $2$ | $1$ |
120.288.8-24.bi.1.19 | $120$ | $3$ | $3$ | $8$ |
120.384.7-24.ba.1.26 | $120$ | $4$ | $4$ | $7$ |
120.480.16-120.w.1.4 | $120$ | $5$ | $5$ | $16$ |