Invariants
Level: | $240$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $4^{8}\cdot16^{4}$ | Cusp orbits | $2^{4}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16J3 |
Level structure
$\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}7&160\\8&181\end{bmatrix}$, $\begin{bmatrix}9&182\\160&61\end{bmatrix}$, $\begin{bmatrix}119&24\\176&137\end{bmatrix}$, $\begin{bmatrix}191&206\\152&193\end{bmatrix}$, $\begin{bmatrix}203&166\\32&165\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.96.3.eh.1 for the level structure with $-I$) |
Cyclic 240-isogeny field degree: | $48$ |
Cyclic 240-torsion field degree: | $3072$ |
Full 240-torsion field degree: | $2949120$ |
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 |
---|---|---|---|---|---|
16.96.2-16.d.1.10 | $16$ | $2$ | $2$ | $2$ | $0$ |
120.96.0-120.da.2.4 | $120$ | $2$ | $2$ | $0$ | $?$ |
240.96.0-120.da.2.16 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.96.1-240.b.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ |
240.96.1-240.b.1.46 | $240$ | $2$ | $2$ | $1$ | $?$ |
240.96.2-16.d.1.10 | $240$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
240.384.5-240.hd.2.4 | $240$ | $2$ | $2$ | $5$ |
240.384.5-240.hf.2.7 | $240$ | $2$ | $2$ | $5$ |
240.384.5-240.im.2.6 | $240$ | $2$ | $2$ | $5$ |
240.384.5-240.in.1.4 | $240$ | $2$ | $2$ | $5$ |
240.384.5-240.kw.2.6 | $240$ | $2$ | $2$ | $5$ |
240.384.5-240.kx.1.4 | $240$ | $2$ | $2$ | $5$ |
240.384.5-240.li.1.4 | $240$ | $2$ | $2$ | $5$ |
240.384.5-240.lj.2.7 | $240$ | $2$ | $2$ | $5$ |