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: | $1 \le \gamma \le 2$ | ||||||
$\overline{\Q}$-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: | $\begin{bmatrix}1&24\\26&7\end{bmatrix}$, $\begin{bmatrix}11&28\\23&107\end{bmatrix}$, $\begin{bmatrix}35&48\\72&89\end{bmatrix}$, $\begin{bmatrix}77&108\\117&95\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.24.0.dy.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
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
8.24.0-8.o.1.4 | $8$ | $2$ | $2$ | $0$ | $0$ |
120.24.0-8.o.1.3 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.24.0-120.s.1.5 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.24.0-120.s.1.16 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.24.0-120.y.1.12 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.24.0-120.y.1.32 | $120$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
120.144.4-120.nm.1.28 | $120$ | $3$ | $3$ | $4$ |
120.192.3-120.qe.1.28 | $120$ | $4$ | $4$ | $3$ |
120.240.8-120.fw.1.8 | $120$ | $5$ | $5$ | $8$ |
120.288.7-120.dwr.1.15 | $120$ | $6$ | $6$ | $7$ |
120.480.15-120.ne.1.32 | $120$ | $10$ | $10$ | $15$ |
240.96.1-240.z.1.9 | $240$ | $2$ | $2$ | $1$ |
240.96.1-240.bb.1.13 | $240$ | $2$ | $2$ | $1$ |
240.96.1-240.ek.1.13 | $240$ | $2$ | $2$ | $1$ |
240.96.1-240.en.1.15 | $240$ | $2$ | $2$ | $1$ |
240.96.1-240.hm.1.11 | $240$ | $2$ | $2$ | $1$ |
240.96.1-240.hp.1.15 | $240$ | $2$ | $2$ | $1$ |
240.96.1-240.id.1.14 | $240$ | $2$ | $2$ | $1$ |
240.96.1-240.if.1.16 | $240$ | $2$ | $2$ | $1$ |