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: | $\begin{bmatrix}24&127\\101&34\end{bmatrix}$, $\begin{bmatrix}48&77\\43&178\end{bmatrix}$, $\begin{bmatrix}65&126\\94&113\end{bmatrix}$, $\begin{bmatrix}66&23\\11&110\end{bmatrix}$, $\begin{bmatrix}235&92\\46&129\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.48.0.eg.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 |
---|---|---|---|---|---|
40.48.0-40.ca.1.9 | $40$ | $2$ | $2$ | $0$ | $0$ |
48.48.0-48.g.1.31 | $48$ | $2$ | $2$ | $0$ | $0$ |
240.48.0-48.g.1.11 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-240.m.1.12 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-240.m.1.33 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-40.ca.1.12 | $240$ | $2$ | $2$ | $0$ | $?$ |
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.s.1.4 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.cf.1.13 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.ed.2.6 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.ez.1.11 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.gn.1.16 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.gt.1.8 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.hf.1.16 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.hh.2.16 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.wp.1.6 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.ww.1.13 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.xu.2.8 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.yd.1.11 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.yy.1.14 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.zl.1.4 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.baj.1.12 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.bam.2.8 | $240$ | $2$ | $2$ | $1$ |
240.288.8-240.xo.2.39 | $240$ | $3$ | $3$ | $8$ |
240.384.7-240.bcf.1.43 | $240$ | $4$ | $4$ | $7$ |
240.480.16-240.fm.1.12 | $240$ | $5$ | $5$ | $16$ |