Invariants
Level: | $240$ | $\SL_2$-level: | $16$ | ||||
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 | $1^{4}\cdot2^{2}\cdot4^{2}\cdot16^{2}$ | 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: | 16H0 |
Level structure
$\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}10&59\\127&94\end{bmatrix}$, $\begin{bmatrix}156&229\\161&40\end{bmatrix}$, $\begin{bmatrix}162&65\\41&218\end{bmatrix}$, $\begin{bmatrix}174&23\\95&78\end{bmatrix}$, $\begin{bmatrix}175&36\\234&137\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.48.0.ct.1 for the level structure with $-I$) |
Cyclic 240-isogeny field degree: | $48$ |
Cyclic 240-torsion field degree: | $1536$ |
Full 240-torsion field degree: | $5898240$ |
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 |
---|---|---|---|---|---|
48.48.0-24.bz.1.7 | $48$ | $2$ | $2$ | $0$ | $0$ |
80.48.0-80.n.2.1 | $80$ | $2$ | $2$ | $0$ | $?$ |
120.48.0-24.bz.1.11 | $120$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-80.n.2.1 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-240.o.1.1 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-240.o.1.57 | $240$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
240.192.1-240.bg.1.11 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.cr.2.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.ep.1.10 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.fk.1.5 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.ji.2.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.jo.2.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.km.1.5 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.kw.1.9 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.lw.2.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.md.2.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.nb.1.5 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.nk.1.3 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.ok.2.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.om.2.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.pk.1.3 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.py.1.5 | $240$ | $2$ | $2$ | $1$ |
240.288.8-240.tp.2.3 | $240$ | $3$ | $3$ | $8$ |
240.384.7-240.yk.1.9 | $240$ | $4$ | $4$ | $7$ |
240.480.16-240.dv.1.3 | $240$ | $5$ | $5$ | $16$ |