Invariants
Level: | $304$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (none of which are rational) | Cusp widths | $2^{8}\cdot4^{4}\cdot16^{4}$ | Cusp orbits | $2^{4}\cdot4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16M1 |
Level structure
$\GL_2(\Z/304\Z)$-generators: | $\begin{bmatrix}71&104\\154&97\end{bmatrix}$, $\begin{bmatrix}85&24\\234&185\end{bmatrix}$, $\begin{bmatrix}209&168\\11&21\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 304.96.1.ej.1 for the level structure with $-I$) |
Cyclic 304-isogeny field degree: | $40$ |
Cyclic 304-torsion field degree: | $1440$ |
Full 304-torsion field degree: | $15759360$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
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 | Kernel decomposition |
---|---|---|---|---|---|---|
16.96.0-16.z.1.2 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
152.96.0-152.bl.2.5 | $152$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
304.96.0-304.y.1.3 | $304$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
304.96.0-304.y.1.10 | $304$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
304.96.0-16.z.1.8 | $304$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
304.96.0-152.bl.2.2 | $304$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
304.96.0-304.bw.2.6 | $304$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
304.96.0-304.bw.2.13 | $304$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
304.96.1-304.bo.2.4 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.bo.2.11 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.br.1.7 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.br.1.13 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.ck.1.12 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.ck.1.15 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |