Invariants
Level: | $120$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
Index: | $240$ | $\PSL_2$-index: | $120$ | ||||
Genus: | $8 = 1 + \frac{ 120 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
Cusps: | $6$ (none of which are rational) | Cusp widths | $10^{4}\cdot40^{2}$ | Cusp orbits | $2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $3 \le \gamma \le 14$ | ||||||
$\overline{\Q}$-gonality: | $3 \le \gamma \le 8$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 40A8 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}9&10\\40&109\end{bmatrix}$, $\begin{bmatrix}59&42\\108&41\end{bmatrix}$, $\begin{bmatrix}77&65\\8&21\end{bmatrix}$, $\begin{bmatrix}117&74\\44&115\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.120.8.ds.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $48$ |
Cyclic 120-torsion field degree: | $1536$ |
Full 120-torsion field degree: | $147456$ |
Rational points
This modular curve has no $\Q_p$ points for $p=7$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
40.120.4-40.bq.1.13 | $40$ | $2$ | $2$ | $4$ | $1$ |
120.48.0-24.bq.1.6 | $120$ | $5$ | $5$ | $0$ | $?$ |
120.120.4-120.be.1.5 | $120$ | $2$ | $2$ | $4$ | $?$ |
120.120.4-120.be.1.14 | $120$ | $2$ | $2$ | $4$ | $?$ |
120.120.4-40.bq.1.7 | $120$ | $2$ | $2$ | $4$ | $?$ |
120.120.4-120.bw.1.13 | $120$ | $2$ | $2$ | $4$ | $?$ |
120.120.4-120.bw.1.22 | $120$ | $2$ | $2$ | $4$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
240.480.17-240.bp.1.13 | $240$ | $2$ | $2$ | $17$ |
240.480.17-240.br.1.13 | $240$ | $2$ | $2$ | $17$ |
240.480.17-240.do.1.15 | $240$ | $2$ | $2$ | $17$ |
240.480.17-240.dp.1.9 | $240$ | $2$ | $2$ | $17$ |
240.480.17-240.ge.1.16 | $240$ | $2$ | $2$ | $17$ |
240.480.17-240.gf.1.13 | $240$ | $2$ | $2$ | $17$ |
240.480.17-240.hj.1.15 | $240$ | $2$ | $2$ | $17$ |
240.480.17-240.hl.1.15 | $240$ | $2$ | $2$ | $17$ |