Invariants
| Level: | $273$ | $\SL_2$-level: | $7$ | ||||
| Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (none of which are rational) | Cusp widths | $1^{3}\cdot7^{3}$ | Cusp orbits | $3^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1 \le \gamma \le 2$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 7E0 |
Level structure
| $\GL_2(\Z/273\Z)$-generators: | $\begin{bmatrix}19&217\\108&134\end{bmatrix}$, $\begin{bmatrix}24&209\\247&76\end{bmatrix}$, $\begin{bmatrix}158&21\\208&107\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 91.24.0.b.1 for the level structure with $-I$) |
| Cyclic 273-isogeny field degree: | $56$ |
| Cyclic 273-torsion field degree: | $8064$ |
| Full 273-torsion field degree: | $52835328$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 21.16.0-7.a.1.2 | $21$ | $3$ | $3$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 273.144.4-273.b.2.14 | $273$ | $3$ | $3$ | $4$ |
| 273.192.3-273.b.1.7 | $273$ | $4$ | $4$ | $3$ |
| 273.336.3-91.b.1.3 | $273$ | $7$ | $7$ | $3$ |