Invariants
| Level: | $104$ | $\SL_2$-level: | $104$ | Newform level: | $1$ | ||
| Index: | $336$ | $\PSL_2$-index: | $168$ | ||||
| Genus: | $11 = 1 + \frac{ 168 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (of which $4$ are rational) | Cusp widths | $1^{2}\cdot2\cdot8\cdot13^{2}\cdot26\cdot104$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 11$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 11$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 104D11 |
Level structure
| $\GL_2(\Z/104\Z)$-generators: | $\begin{bmatrix}9&100\\60&101\end{bmatrix}$, $\begin{bmatrix}16&3\\7&12\end{bmatrix}$, $\begin{bmatrix}28&23\\85&18\end{bmatrix}$, $\begin{bmatrix}53&8\\102&11\end{bmatrix}$, $\begin{bmatrix}81&44\\90&87\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 104.168.11.bw.1 for the level structure with $-I$) |
| Cyclic 104-isogeny field degree: | $2$ |
| Cyclic 104-torsion field degree: | $48$ |
| Full 104-torsion field degree: | $119808$ |
Rational points
This modular curve has 4 rational cusps but no known non-cuspidal rational points.
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.24.0-8.m.1.8 | $8$ | $14$ | $14$ | $0$ | $0$ |
| $X_0(13)$ | $13$ | $24$ | $12$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.24.0-8.m.1.8 | $8$ | $14$ | $14$ | $0$ | $0$ |
| 52.168.5-52.c.1.4 | $52$ | $2$ | $2$ | $5$ | $0$ |
| 104.168.5-52.c.1.22 | $104$ | $2$ | $2$ | $5$ | $?$ |