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: | $\begin{bmatrix}32&53\\41&156\end{bmatrix}$, $\begin{bmatrix}59&196\\22&225\end{bmatrix}$, $\begin{bmatrix}64&89\\159&2\end{bmatrix}$, $\begin{bmatrix}77&24\\52&185\end{bmatrix}$, $\begin{bmatrix}208&69\\15&46\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.48.0.dp.1 for the level structure with $-I$) |
Cyclic 240-isogeny field degree: | $48$ |
Cyclic 240-torsion field degree: | $3072$ |
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 |
---|---|---|---|---|---|
48.48.0-48.e.1.29 | $48$ | $2$ | $2$ | $0$ | $0$ |
80.48.0-80.o.1.21 | $80$ | $2$ | $2$ | $0$ | $?$ |
120.48.0-120.ej.1.20 | $120$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-48.e.1.7 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-80.o.1.2 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-120.ej.1.21 | $240$ | $2$ | $2$ | $0$ | $?$ |
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.bv.1.16 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.ci.2.11 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.ds.1.23 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.fg.2.14 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.ht.2.9 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.hy.2.15 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.ik.2.10 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.in.2.8 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.qo.2.16 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.qx.1.14 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.rn.2.16 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.sk.1.16 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.sv.1.13 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.tm.2.15 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.uc.1.14 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.ur.2.8 | $240$ | $2$ | $2$ | $1$ |
240.288.8-240.vd.2.59 | $240$ | $3$ | $3$ | $8$ |
240.384.7-240.zy.1.53 | $240$ | $4$ | $4$ | $7$ |
240.480.16-240.er.2.27 | $240$ | $5$ | $5$ | $16$ |