Invariants
| Level: | $304$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (all of which are rational) | Cusp widths | $2^{2}\cdot4\cdot16$ | Cusp orbits | $1^{4}$ | ||
| 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: | 16A1 |
Level structure
| $\GL_2(\Z/304\Z)$-generators: | $\begin{bmatrix}0&143\\107&92\end{bmatrix}$, $\begin{bmatrix}83&284\\12&11\end{bmatrix}$, $\begin{bmatrix}136&243\\49&198\end{bmatrix}$, $\begin{bmatrix}196&271\\207&132\end{bmatrix}$, $\begin{bmatrix}239&204\\210&205\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 304.24.1.a.1 for the level structure with $-I$) |
| Cyclic 304-isogeny field degree: | $40$ |
| Cyclic 304-torsion field degree: | $2880$ |
| Full 304-torsion field degree: | $63037440$ |
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 |
|---|---|---|---|---|---|---|
| 16.24.0-8.n.1.8 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 152.24.0-8.n.1.2 | $152$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 304.96.1-304.a.2.10 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 304.96.1-304.d.1.10 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 304.96.1-304.g.1.4 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 304.96.1-304.i.1.2 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 304.96.1-304.bo.1.2 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 304.96.1-304.bo.2.1 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 304.96.1-304.bp.1.1 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 304.96.1-304.bp.2.2 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 304.96.1-304.bq.1.2 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 304.96.1-304.bq.2.1 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 304.96.1-304.br.1.1 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 304.96.1-304.br.2.3 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 304.96.1-304.bs.1.1 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 304.96.1-304.bs.2.5 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 304.96.1-304.bt.1.1 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 304.96.1-304.bt.2.2 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 304.96.1-304.bu.1.1 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 304.96.1-304.bu.2.3 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 304.96.1-304.bv.1.1 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 304.96.1-304.bv.2.2 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 304.96.1-304.cf.1.10 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 304.96.1-304.cg.1.10 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 304.96.1-304.cj.1.2 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 304.96.1-304.ck.1.2 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |