Invariants
Level: | $304$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot16^{2}$ | Cusp orbits | $2^{2}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 48$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16E1 |
Level structure
$\GL_2(\Z/304\Z)$-generators: | $\begin{bmatrix}123&60\\61&205\end{bmatrix}$, $\begin{bmatrix}171&296\\268&207\end{bmatrix}$, $\begin{bmatrix}173&180\\177&95\end{bmatrix}$, $\begin{bmatrix}189&212\\107&231\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 304.48.1.m.1 for the level structure with $-I$) |
Cyclic 304-isogeny field degree: | $80$ |
Cyclic 304-torsion field degree: | $11520$ |
Full 304-torsion field degree: | $31518720$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
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 | Kernel decomposition |
---|---|---|---|---|---|---|
8.48.0-8.w.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
304.48.0-304.j.1.3 | $304$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
304.48.0-304.j.1.10 | $304$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
304.48.0-8.w.1.1 | $304$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
304.48.1-304.c.1.7 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.48.1-304.c.1.14 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
304.192.3-304.in.1.4 | $304$ | $2$ | $2$ | $3$ | $?$ | not computed |
304.192.3-304.io.1.4 | $304$ | $2$ | $2$ | $3$ | $?$ | not computed |
304.192.3-304.is.1.7 | $304$ | $2$ | $2$ | $3$ | $?$ | not computed |
304.192.3-304.it.1.4 | $304$ | $2$ | $2$ | $3$ | $?$ | not computed |