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: | $\begin{bmatrix}76&61\\3&86\end{bmatrix}$, $\begin{bmatrix}84&113\\163&74\end{bmatrix}$, $\begin{bmatrix}94&95\\231&134\end{bmatrix}$, $\begin{bmatrix}99&22\\236&37\end{bmatrix}$, $\begin{bmatrix}121&0\\110&211\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.48.0.cx.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 |
---|---|---|---|---|---|
16.48.0-16.f.1.4 | $16$ | $2$ | $2$ | $0$ | $0$ |
120.48.0-120.ej.1.5 | $120$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-16.f.1.5 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-240.o.1.3 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-240.o.1.63 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-120.ej.1.19 | $240$ | $2$ | $2$ | $0$ | $?$ |
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.cb.2.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.ct.2.7 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.ew.1.15 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.fo.1.8 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.jj.2.4 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.js.2.13 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.kq.1.8 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.kx.1.12 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.ly.2.5 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.mf.2.2 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.nd.1.10 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.nm.2.6 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.oj.2.5 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.os.2.5 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.pq.2.7 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.px.1.10 | $240$ | $2$ | $2$ | $1$ |
240.288.8-240.tt.2.31 | $240$ | $3$ | $3$ | $8$ |
240.384.7-240.yo.1.7 | $240$ | $4$ | $4$ | $7$ |
240.480.16-240.dz.2.31 | $240$ | $5$ | $5$ | $16$ |