Invariants
| Level: | $304$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $2 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 14 }{2}$ | ||||||
| Cusps: | $14$ (of which $2$ are rational) | Cusp widths | $4^{8}\cdot8^{4}\cdot16^{2}$ | Cusp orbits | $1^{2}\cdot2^{4}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16I2 |
Level structure
| $\GL_2(\Z/304\Z)$-generators: | $\begin{bmatrix}7&164\\264&187\end{bmatrix}$, $\begin{bmatrix}17&172\\36&249\end{bmatrix}$, $\begin{bmatrix}175&272\\8&105\end{bmatrix}$, $\begin{bmatrix}191&272\\132&95\end{bmatrix}$, $\begin{bmatrix}257&268\\76&53\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 304.96.2.d.1 for the level structure with $-I$) |
| Cyclic 304-isogeny field degree: | $80$ |
| Cyclic 304-torsion field degree: | $5760$ |
| Full 304-torsion field degree: | $15759360$ |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.96.0-8.c.1.4 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 304.96.0-8.c.1.1 | $304$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 304.384.5-304.p.1.10 | $304$ | $2$ | $2$ | $5$ |
| 304.384.5-304.p.2.13 | $304$ | $2$ | $2$ | $5$ |
| 304.384.5-304.t.1.12 | $304$ | $2$ | $2$ | $5$ |
| 304.384.5-304.t.2.14 | $304$ | $2$ | $2$ | $5$ |
| 304.384.5-304.bo.1.16 | $304$ | $2$ | $2$ | $5$ |
| 304.384.5-304.bo.4.18 | $304$ | $2$ | $2$ | $5$ |
| 304.384.5-304.bs.1.12 | $304$ | $2$ | $2$ | $5$ |
| 304.384.5-304.bs.2.12 | $304$ | $2$ | $2$ | $5$ |
| 304.384.5-304.cx.1.14 | $304$ | $2$ | $2$ | $5$ |
| 304.384.5-304.cx.2.14 | $304$ | $2$ | $2$ | $5$ |
| 304.384.5-304.cz.1.16 | $304$ | $2$ | $2$ | $5$ |
| 304.384.5-304.cz.2.19 | $304$ | $2$ | $2$ | $5$ |
| 304.384.5-304.dd.1.14 | $304$ | $2$ | $2$ | $5$ |
| 304.384.5-304.dd.2.12 | $304$ | $2$ | $2$ | $5$ |
| 304.384.5-304.dh.1.15 | $304$ | $2$ | $2$ | $5$ |
| 304.384.5-304.dh.2.15 | $304$ | $2$ | $2$ | $5$ |
| 304.384.7-304.l.1.10 | $304$ | $2$ | $2$ | $7$ |
| 304.384.7-304.n.1.13 | $304$ | $2$ | $2$ | $7$ |
| 304.384.7-304.q.1.18 | $304$ | $2$ | $2$ | $7$ |
| 304.384.7-304.t.1.14 | $304$ | $2$ | $2$ | $7$ |
| 304.384.7-304.bc.1.5 | $304$ | $2$ | $2$ | $7$ |
| 304.384.7-304.bd.1.2 | $304$ | $2$ | $2$ | $7$ |
| 304.384.7-304.bh.1.6 | $304$ | $2$ | $2$ | $7$ |
| 304.384.7-304.bj.1.3 | $304$ | $2$ | $2$ | $7$ |