Invariants
Level: | $120$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
Index: | $120$ | $\PSL_2$-index: | $60$ | ||||
Genus: | $4 = 1 + \frac{ 60 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (of which $2$ are rational) | Cusp widths | $10^{2}\cdot20^{2}$ | Cusp orbits | $1^{2}\cdot2$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 4$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 20A4 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}21&22\\110&33\end{bmatrix}$, $\begin{bmatrix}37&88\\106&41\end{bmatrix}$, $\begin{bmatrix}43&106\\38&67\end{bmatrix}$, $\begin{bmatrix}91&34\\8&9\end{bmatrix}$, $\begin{bmatrix}119&12\\28&101\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.60.4.c.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $96$ |
Cyclic 120-torsion field degree: | $3072$ |
Full 120-torsion field degree: | $294912$ |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
40.60.2-10.a.1.2 | $40$ | $2$ | $2$ | $2$ | $0$ |
60.60.2-10.a.1.1 | $60$ | $2$ | $2$ | $2$ | $0$ |
120.24.0-120.a.1.7 | $120$ | $5$ | $5$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
120.240.8-120.h.1.3 | $120$ | $2$ | $2$ | $8$ |
120.240.8-120.h.1.15 | $120$ | $2$ | $2$ | $8$ |
120.240.8-120.i.1.4 | $120$ | $2$ | $2$ | $8$ |
120.240.8-120.i.1.6 | $120$ | $2$ | $2$ | $8$ |
120.240.8-120.l.1.3 | $120$ | $2$ | $2$ | $8$ |
120.240.8-120.l.1.20 | $120$ | $2$ | $2$ | $8$ |
120.240.8-120.n.1.3 | $120$ | $2$ | $2$ | $8$ |
120.240.8-120.n.1.11 | $120$ | $2$ | $2$ | $8$ |
120.240.8-120.o.1.9 | $120$ | $2$ | $2$ | $8$ |
120.240.8-120.o.1.12 | $120$ | $2$ | $2$ | $8$ |
120.240.8-120.p.1.3 | $120$ | $2$ | $2$ | $8$ |
120.240.8-120.p.1.5 | $120$ | $2$ | $2$ | $8$ |
120.240.8-120.x.1.1 | $120$ | $2$ | $2$ | $8$ |
120.240.8-120.x.1.11 | $120$ | $2$ | $2$ | $8$ |
120.240.8-120.y.1.10 | $120$ | $2$ | $2$ | $8$ |
120.240.8-120.y.1.11 | $120$ | $2$ | $2$ | $8$ |
120.360.10-120.c.1.27 | $120$ | $3$ | $3$ | $10$ |
120.360.14-120.g.1.4 | $120$ | $3$ | $3$ | $14$ |
120.480.13-120.ee.1.9 | $120$ | $4$ | $4$ | $13$ |
120.480.17-120.fm.1.14 | $120$ | $4$ | $4$ | $17$ |