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: | $\begin{bmatrix}38&27\\43&230\end{bmatrix}$, $\begin{bmatrix}48&17\\175&18\end{bmatrix}$, $\begin{bmatrix}61&120\\4&161\end{bmatrix}$, $\begin{bmatrix}111&226\\220&53\end{bmatrix}$, $\begin{bmatrix}160&167\\23&56\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.48.0.dn.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.2.1 | $16$ | $2$ | $2$ | $0$ | $0$ |
120.48.0-120.ej.1.4 | $120$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-16.f.2.3 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-240.p.1.1 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-240.p.1.4 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-120.ej.1.2 | $240$ | $2$ | $2$ | $0$ | $?$ |
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.by.2.2 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.db.1.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.ev.2.4 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.fw.1.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.jc.2.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.jz.1.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.kh.2.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.lg.1.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.lq.2.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.mn.1.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.mv.2.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.nu.1.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.oc.2.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.oz.1.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.ph.2.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.qg.1.1 | $240$ | $2$ | $2$ | $1$ |
240.288.8-240.uz.2.7 | $240$ | $3$ | $3$ | $8$ |
240.384.7-240.ze.1.1 | $240$ | $4$ | $4$ | $7$ |
240.480.16-240.ep.1.1 | $240$ | $5$ | $5$ | $16$ |