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 | $2^{4}\cdot4^{2}\cdot8^{4}$ | 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: | 8O0 |
Level structure
$\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}19&88\\178&75\end{bmatrix}$, $\begin{bmatrix}103&120\\226&223\end{bmatrix}$, $\begin{bmatrix}145&96\\127&85\end{bmatrix}$, $\begin{bmatrix}147&40\\79&229\end{bmatrix}$, $\begin{bmatrix}169&176\\10&159\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.48.0.du.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.2.13 | $48$ | $2$ | $2$ | $0$ | $0$ |
80.48.0-40.bj.1.7 | $80$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-40.bj.1.6 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-24.bz.2.1 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-120.ej.2.2 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-120.ej.2.29 | $240$ | $2$ | $2$ | $0$ | $?$ |
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.hq.1.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.hs.1.9 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.hy.1.9 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.ia.1.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.nw.1.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.oc.1.9 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.om.1.9 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.os.1.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.wm.1.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.ws.1.9 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.xc.1.9 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.xi.1.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.bbk.1.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.bbm.1.9 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.bbs.1.9 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.bbu.1.1 | $240$ | $2$ | $2$ | $1$ |
240.288.8-120.ri.1.12 | $240$ | $3$ | $3$ | $8$ |
240.384.7-120.lh.2.11 | $240$ | $4$ | $4$ | $7$ |
240.480.16-120.fp.1.5 | $240$ | $5$ | $5$ | $16$ |