Invariants
Level: | $120$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $2 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
Cusps: | $6$ (all of which are rational) | Cusp widths | $2^{2}\cdot6^{2}\cdot8\cdot24$ | Cusp orbits | $1^{6}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $6$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24F2 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}20&39\\23&40\end{bmatrix}$, $\begin{bmatrix}64&83\\69&62\end{bmatrix}$, $\begin{bmatrix}67&86\\54&71\end{bmatrix}$, $\begin{bmatrix}76&113\\9&56\end{bmatrix}$, $\begin{bmatrix}97&84\\18&67\end{bmatrix}$, $\begin{bmatrix}98&97\\89&90\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.48.2.i.2 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $12$ |
Cyclic 120-torsion field degree: | $384$ |
Full 120-torsion field degree: | $368640$ |
Rational points
This modular curve has 6 rational cusps but no known non-cuspidal rational points.
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
Factor curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
3.8.0-3.a.1.1 | $3$ | $12$ | $12$ | $0$ | $0$ |
40.12.0-4.c.1.6 | $40$ | $8$ | $8$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
12.48.0-12.g.1.10 | $12$ | $2$ | $2$ | $0$ | $0$ |
120.48.0-12.g.1.20 | $120$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.