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: | $16$ (of which $4$ are rational) | Cusp widths | $2^{8}\cdot4^{4}\cdot16^{4}$ | Cusp orbits | $1^{4}\cdot4^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16M1 |
Level structure
$\GL_2(\Z/304\Z)$-generators: | $\begin{bmatrix}121&128\\194&161\end{bmatrix}$, $\begin{bmatrix}129&160\\289&279\end{bmatrix}$, $\begin{bmatrix}243&16\\20&223\end{bmatrix}$, $\begin{bmatrix}255&104\\156&251\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 304.96.1.bg.2 for the level structure with $-I$) |
Cyclic 304-isogeny field degree: | $40$ |
Cyclic 304-torsion field degree: | $2880$ |
Full 304-torsion field degree: | $15759360$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
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.j.1.4 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
152.96.0-152.bd.2.6 | $152$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
304.96.0-16.j.1.10 | $304$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
304.96.0-304.bc.1.7 | $304$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
304.96.0-304.bc.1.9 | $304$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
304.96.0-152.bd.2.7 | $304$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
304.96.0-304.bd.1.6 | $304$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
304.96.0-304.bd.1.9 | $304$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
304.96.1-304.h.1.1 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.h.1.16 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.bw.1.7 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.bw.1.9 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.bx.1.7 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.bx.1.9 | $304$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
304.384.5-304.gm.2.1 | $304$ | $2$ | $2$ | $5$ | $?$ | not computed |
304.384.5-304.go.1.3 | $304$ | $2$ | $2$ | $5$ | $?$ | not computed |
304.384.5-304.gp.1.1 | $304$ | $2$ | $2$ | $5$ | $?$ | not computed |
304.384.5-304.gs.1.4 | $304$ | $2$ | $2$ | $5$ | $?$ | not computed |