Invariants
| Level: | $328$ | $\SL_2$-level: | $8$ | ||||
| Index: | $24$ | $\PSL_2$-index: | $12$ | ||||
| Genus: | $0 = 1 + \frac{ 12 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (of which $2$ are rational) | Cusp widths | $1^{2}\cdot2\cdot8$ | Cusp orbits | $1^{2}\cdot2$ | ||
| 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: | 8C0 |
Level structure
| $\GL_2(\Z/328\Z)$-generators: | $\begin{bmatrix}12&235\\281&74\end{bmatrix}$, $\begin{bmatrix}33&212\\120&65\end{bmatrix}$, $\begin{bmatrix}57&190\\114&297\end{bmatrix}$, $\begin{bmatrix}172&25\\149&196\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 328.12.0.bb.1 for the level structure with $-I$) |
| Cyclic 328-isogeny field degree: | $84$ |
| Cyclic 328-torsion field degree: | $13440$ |
| Full 328-torsion field degree: | $176332800$ |
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 |
|---|---|---|---|---|---|
| 8.12.0-4.c.1.3 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 328.12.0-4.c.1.3 | $328$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 328.48.0-328.l.1.10 | $328$ | $2$ | $2$ | $0$ |
| 328.48.0-328.o.1.7 | $328$ | $2$ | $2$ | $0$ |
| 328.48.0-328.bf.1.2 | $328$ | $2$ | $2$ | $0$ |
| 328.48.0-328.bg.1.1 | $328$ | $2$ | $2$ | $0$ |
| 328.48.0-328.bi.1.2 | $328$ | $2$ | $2$ | $0$ |
| 328.48.0-328.bl.1.3 | $328$ | $2$ | $2$ | $0$ |
| 328.48.0-328.bx.1.6 | $328$ | $2$ | $2$ | $0$ |
| 328.48.0-328.by.1.8 | $328$ | $2$ | $2$ | $0$ |