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 | $2^{8}\cdot16^{2}$ | 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: | 16G0 |
Level structure
$\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}37&112\\23&217\end{bmatrix}$, $\begin{bmatrix}51&152\\58&209\end{bmatrix}$, $\begin{bmatrix}57&224\\35&199\end{bmatrix}$, $\begin{bmatrix}183&104\\22&133\end{bmatrix}$, $\begin{bmatrix}205&144\\86&139\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.48.0.bb.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.bh.1.1 | $48$ | $2$ | $2$ | $0$ | $0$ |
80.48.0-80.n.1.17 | $80$ | $2$ | $2$ | $0$ | $?$ |
120.48.0-24.bh.1.4 | $120$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-240.m.2.2 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-240.m.2.61 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-80.n.1.18 | $240$ | $2$ | $2$ | $0$ | $?$ |
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.gl.1.9 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.gm.2.3 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.gt.2.3 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.gu.1.9 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.ln.1.9 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.lo.2.3 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.lv.2.3 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.lw.1.9 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.ql.2.3 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.qm.1.5 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.qt.1.5 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.qu.2.3 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.vh.2.3 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.vi.1.5 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.vp.1.5 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.vq.2.3 | $240$ | $2$ | $2$ | $1$ |
240.288.8-240.ed.1.33 | $240$ | $3$ | $3$ | $8$ |
240.384.7-240.qf.2.25 | $240$ | $4$ | $4$ | $7$ |
240.480.16-240.bw.1.18 | $240$ | $5$ | $5$ | $16$ |