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: | $\begin{bmatrix}61&216\\195&217\end{bmatrix}$, $\begin{bmatrix}67&32\\65&93\end{bmatrix}$, $\begin{bmatrix}93&8\\223&31\end{bmatrix}$, $\begin{bmatrix}189&112\\163&17\end{bmatrix}$, $\begin{bmatrix}209&112\\229&163\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.48.0.bm.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.bn.1.12 | $40$ | $2$ | $2$ | $0$ | $0$ |
48.48.0-48.e.2.22 | $48$ | $2$ | $2$ | $0$ | $0$ |
240.48.0-48.e.2.1 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-240.m.2.5 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-240.m.2.56 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.48.0-40.bn.1.1 | $240$ | $2$ | $2$ | $0$ | $?$ |
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.if.1.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.ig.1.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.in.1.5 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.io.1.5 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.pd.1.9 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.pe.1.2 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.pt.1.6 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.pu.1.11 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.xt.1.6 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.xu.1.7 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.yj.1.5 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.yk.1.2 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.bbz.1.12 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.bca.1.8 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.bch.1.6 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.bci.1.10 | $240$ | $2$ | $2$ | $1$ |
240.288.8-240.fh.1.55 | $240$ | $3$ | $3$ | $8$ |
240.384.7-240.sm.2.36 | $240$ | $4$ | $4$ | $7$ |
240.480.16-240.co.2.8 | $240$ | $5$ | $5$ | $16$ |