Invariants
| Level: | $304$ | $\SL_2$-level: | $16$ | ||||
| Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $1^{2}\cdot2^{3}\cdot16$ | Cusp orbits | $1^{2}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16D0 |
Level structure
| $\GL_2(\Z/304\Z)$-generators: | $\begin{bmatrix}15&272\\130&77\end{bmatrix}$, $\begin{bmatrix}46&157\\63&116\end{bmatrix}$, $\begin{bmatrix}173&190\\230&29\end{bmatrix}$, $\begin{bmatrix}253&296\\52&97\end{bmatrix}$, $\begin{bmatrix}292&11\\171&148\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 304.24.0.f.2 for the level structure with $-I$) |
| Cyclic 304-isogeny field degree: | $40$ |
| Cyclic 304-torsion field degree: | $2880$ |
| Full 304-torsion field degree: | $63037440$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 16.24.0-8.n.1.8 | $16$ | $2$ | $2$ | $0$ | $0$ |
| 152.24.0-8.n.1.8 | $152$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 304.96.0-304.d.1.18 | $304$ | $2$ | $2$ | $0$ |
| 304.96.0-304.f.1.9 | $304$ | $2$ | $2$ | $0$ |
| 304.96.0-304.k.1.5 | $304$ | $2$ | $2$ | $0$ |
| 304.96.0-304.l.2.10 | $304$ | $2$ | $2$ | $0$ |
| 304.96.0-304.u.1.9 | $304$ | $2$ | $2$ | $0$ |
| 304.96.0-304.x.2.9 | $304$ | $2$ | $2$ | $0$ |
| 304.96.0-304.z.1.9 | $304$ | $2$ | $2$ | $0$ |
| 304.96.0-304.ba.2.10 | $304$ | $2$ | $2$ | $0$ |
| 304.96.0-304.bg.1.1 | $304$ | $2$ | $2$ | $0$ |
| 304.96.0-304.bh.1.2 | $304$ | $2$ | $2$ | $0$ |
| 304.96.0-304.bo.1.2 | $304$ | $2$ | $2$ | $0$ |
| 304.96.0-304.bp.2.1 | $304$ | $2$ | $2$ | $0$ |
| 304.96.0-304.bu.1.1 | $304$ | $2$ | $2$ | $0$ |
| 304.96.0-304.bv.1.2 | $304$ | $2$ | $2$ | $0$ |
| 304.96.0-304.by.1.2 | $304$ | $2$ | $2$ | $0$ |
| 304.96.0-304.bz.2.1 | $304$ | $2$ | $2$ | $0$ |
| 304.96.1-304.bi.1.1 | $304$ | $2$ | $2$ | $1$ |
| 304.96.1-304.bj.1.3 | $304$ | $2$ | $2$ | $1$ |
| 304.96.1-304.bm.1.3 | $304$ | $2$ | $2$ | $1$ |
| 304.96.1-304.bn.1.1 | $304$ | $2$ | $2$ | $1$ |
| 304.96.1-304.bs.1.1 | $304$ | $2$ | $2$ | $1$ |
| 304.96.1-304.bt.1.3 | $304$ | $2$ | $2$ | $1$ |
| 304.96.1-304.ca.1.3 | $304$ | $2$ | $2$ | $1$ |
| 304.96.1-304.cb.1.1 | $304$ | $2$ | $2$ | $1$ |