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: | $\begin{bmatrix}61&148\\16&161\end{bmatrix}$, $\begin{bmatrix}101&102\\32&227\end{bmatrix}$, $\begin{bmatrix}190&89\\43&156\end{bmatrix}$, $\begin{bmatrix}203&194\\84&121\end{bmatrix}$, $\begin{bmatrix}226&195\\139&58\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 80.48.0.bw.2 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 |
---|---|---|---|---|---|
24.48.0-8.ba.1.7 | $24$ | $2$ | $2$ | $0$ | $0$ |
240.48.0-80.n.1.23 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-80.n.1.28 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-80.p.1.24 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-80.p.1.32 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-8.ba.1.6 | $240$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
240.192.1-80.d.1.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-80.ba.2.8 | $240$ | $2$ | $2$ | $1$ |
240.192.1-80.bm.2.6 | $240$ | $2$ | $2$ | $1$ |
240.192.1-80.bx.2.4 | $240$ | $2$ | $2$ | $1$ |
240.192.1-80.ce.1.8 | $240$ | $2$ | $2$ | $1$ |
240.192.1-80.cs.1.6 | $240$ | $2$ | $2$ | $1$ |
240.192.1-80.cw.2.8 | $240$ | $2$ | $2$ | $1$ |
240.192.1-80.dg.2.2 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.qt.1.4 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.rj.1.2 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.rz.2.13 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.sp.1.2 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.td.1.3 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.tv.1.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.ul.2.9 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.uz.1.1 | $240$ | $2$ | $2$ | $1$ |
240.288.8-240.xg.1.30 | $240$ | $3$ | $3$ | $8$ |
240.384.7-240.bav.1.18 | $240$ | $4$ | $4$ | $7$ |
240.480.16-80.cq.2.8 | $240$ | $5$ | $5$ | $16$ |