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 | $1^{2}\cdot2\cdot4\cdot8^{2}$ | 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: | 8I0 |
Level structure
| $\GL_2(\Z/304\Z)$-generators: | $\begin{bmatrix}0&245\\121&236\end{bmatrix}$, $\begin{bmatrix}45&230\\34&169\end{bmatrix}$, $\begin{bmatrix}81&26\\148&159\end{bmatrix}$, $\begin{bmatrix}134&173\\65&298\end{bmatrix}$, $\begin{bmatrix}283&174\\62&107\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 152.24.0.bu.1 for the level structure with $-I$) |
| Cyclic 304-isogeny field degree: | $40$ |
| Cyclic 304-torsion field degree: | $2880$ |
| Full 304-torsion field degree: | $63037440$ |
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 | $16$ | $2$ | $2$ | $0$ | $0$ |
| 304.24.0-8.n.1.3 | $304$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 304.96.0-152.z.1.4 | $304$ | $2$ | $2$ | $0$ |
| 304.96.0-152.bc.2.1 | $304$ | $2$ | $2$ | $0$ |
| 304.96.0-152.bd.1.7 | $304$ | $2$ | $2$ | $0$ |
| 304.96.0-152.be.1.5 | $304$ | $2$ | $2$ | $0$ |
| 304.96.0-152.bg.1.7 | $304$ | $2$ | $2$ | $0$ |
| 304.96.0-152.bj.1.5 | $304$ | $2$ | $2$ | $0$ |
| 304.96.0-152.bl.1.8 | $304$ | $2$ | $2$ | $0$ |
| 304.96.0-152.bm.1.7 | $304$ | $2$ | $2$ | $0$ |
| 304.96.0-304.bc.2.1 | $304$ | $2$ | $2$ | $0$ |
| 304.96.0-304.bi.2.1 | $304$ | $2$ | $2$ | $0$ |
| 304.96.0-304.bk.1.1 | $304$ | $2$ | $2$ | $0$ |
| 304.96.0-304.bq.1.1 | $304$ | $2$ | $2$ | $0$ |
| 304.96.0-304.bs.2.1 | $304$ | $2$ | $2$ | $0$ |
| 304.96.0-304.bu.2.1 | $304$ | $2$ | $2$ | $0$ |
| 304.96.0-304.bw.1.1 | $304$ | $2$ | $2$ | $0$ |
| 304.96.0-304.by.1.1 | $304$ | $2$ | $2$ | $0$ |
| 304.96.1-304.bg.1.1 | $304$ | $2$ | $2$ | $1$ |
| 304.96.1-304.bi.1.1 | $304$ | $2$ | $2$ | $1$ |
| 304.96.1-304.bk.2.1 | $304$ | $2$ | $2$ | $1$ |
| 304.96.1-304.bm.2.1 | $304$ | $2$ | $2$ | $1$ |
| 304.96.1-304.bo.1.1 | $304$ | $2$ | $2$ | $1$ |
| 304.96.1-304.bu.1.1 | $304$ | $2$ | $2$ | $1$ |
| 304.96.1-304.bw.2.1 | $304$ | $2$ | $2$ | $1$ |
| 304.96.1-304.cc.2.1 | $304$ | $2$ | $2$ | $1$ |