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: | $\begin{bmatrix}131&82\\24&181\end{bmatrix}$, $\begin{bmatrix}187&128\\88&205\end{bmatrix}$, $\begin{bmatrix}189&80\\160&217\end{bmatrix}$, $\begin{bmatrix}209&100\\168&17\end{bmatrix}$, $\begin{bmatrix}225&218\\224&77\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.96.3.id.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 |
---|---|---|---|---|---|
24.96.0-24.bc.1.3 | $24$ | $2$ | $2$ | $0$ | $0$ |
80.96.2-80.f.2.5 | $80$ | $2$ | $2$ | $2$ | $?$ |
240.96.0-24.bc.1.4 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.96.1-240.b.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ |
240.96.1-240.b.1.44 | $240$ | $2$ | $2$ | $1$ | $?$ |
240.96.2-80.f.2.9 | $240$ | $2$ | $2$ | $2$ | $?$ |
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.hw.3.4 | $240$ | $2$ | $2$ | $5$ |
240.384.5-240.ll.2.4 | $240$ | $2$ | $2$ | $5$ |
240.384.5-240.sw.1.4 | $240$ | $2$ | $2$ | $5$ |
240.384.5-240.uc.1.4 | $240$ | $2$ | $2$ | $5$ |
240.384.5-240.bdr.1.4 | $240$ | $2$ | $2$ | $5$ |
240.384.5-240.bfk.1.4 | $240$ | $2$ | $2$ | $5$ |
240.384.5-240.bfs.2.4 | $240$ | $2$ | $2$ | $5$ |
240.384.5-240.bge.2.4 | $240$ | $2$ | $2$ | $5$ |