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: | $\begin{bmatrix}67&16\\128&21\end{bmatrix}$, $\begin{bmatrix}71&12\\96&229\end{bmatrix}$, $\begin{bmatrix}135&14\\16&221\end{bmatrix}$, $\begin{bmatrix}181&122\\224&237\end{bmatrix}$, $\begin{bmatrix}219&38\\8&57\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.96.3.ie.2 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 real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
48.96.1-48.b.1.2 | $48$ | $2$ | $2$ | $1$ | $0$ |
80.96.2-80.f.2.5 | $80$ | $2$ | $2$ | $2$ | $?$ |
120.96.0-120.cy.2.8 | $120$ | $2$ | $2$ | $0$ | $?$ |
240.96.0-120.cy.2.11 | $240$ | $2$ | $2$ | $0$ | $?$ |
240.96.1-48.b.1.24 | $240$ | $2$ | $2$ | $1$ | $?$ |
240.96.2-80.f.2.3 | $240$ | $2$ | $2$ | $2$ | $?$ |
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.gk.1.8 | $240$ | $2$ | $2$ | $5$ |
240.384.5-240.lt.2.4 | $240$ | $2$ | $2$ | $5$ |
240.384.5-240.sf.2.14 | $240$ | $2$ | $2$ | $5$ |
240.384.5-240.uk.2.6 | $240$ | $2$ | $2$ | $5$ |
240.384.5-240.bem.2.15 | $240$ | $2$ | $2$ | $5$ |
240.384.5-240.bfc.2.7 | $240$ | $2$ | $2$ | $5$ |
240.384.5-240.bfy.1.8 | $240$ | $2$ | $2$ | $5$ |
240.384.5-240.bgc.2.4 | $240$ | $2$ | $2$ | $5$ |