Invariants
| Level: | $273$ | $\SL_2$-level: | $91$ | Newform level: | $1$ | ||
| Index: | $224$ | $\PSL_2$-index: | $112$ | ||||
| Genus: | $7 = 1 + \frac{ 112 }{12} - \frac{ 0 }{4} - \frac{ 4 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (all of which are rational) | Cusp widths | $1\cdot7\cdot13\cdot91$ | Cusp orbits | $1^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $4$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 7$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 7$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 91A7 |
Level structure
| $\GL_2(\Z/273\Z)$-generators: | $\begin{bmatrix}7&122\\33&61\end{bmatrix}$, $\begin{bmatrix}252&163\\193&152\end{bmatrix}$, $\begin{bmatrix}260&229\\125&0\end{bmatrix}$, $\begin{bmatrix}272&63\\172&212\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 91.112.7.a.1 for the level structure with $-I$) |
| Cyclic 273-isogeny field degree: | $4$ |
| Cyclic 273-torsion field degree: | $576$ |
| Full 273-torsion field degree: | $11321856$ |
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 |
|---|---|---|---|---|---|
| $X_0(13)$ | $13$ | $16$ | $8$ | $0$ | $0$ |
| 21.16.0-7.a.1.1 | $21$ | $14$ | $14$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 21.16.0-7.a.1.1 | $21$ | $14$ | $14$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 273.448.13-91.a.1.5 | $273$ | $2$ | $2$ | $13$ |
| 273.448.13-91.a.2.5 | $273$ | $2$ | $2$ | $13$ |
| 273.448.13-273.a.1.6 | $273$ | $2$ | $2$ | $13$ |
| 273.448.13-273.a.2.6 | $273$ | $2$ | $2$ | $13$ |
| 273.448.13-91.b.1.3 | $273$ | $2$ | $2$ | $13$ |
| 273.448.13-91.b.2.3 | $273$ | $2$ | $2$ | $13$ |
| 273.448.13-273.b.1.8 | $273$ | $2$ | $2$ | $13$ |
| 273.448.13-273.b.2.8 | $273$ | $2$ | $2$ | $13$ |