Invariants
Level: | $273$ | $\SL_2$-level: | $21$ | Newform level: | $1$ | ||
Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
Genus: | $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
Cusps: | $24$ (none of which are rational) | Cusp widths | $1^{6}\cdot3^{6}\cdot7^{6}\cdot21^{6}$ | Cusp orbits | $3^{2}\cdot6^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $3 \le \gamma \le 8$ | ||||||
$\overline{\Q}$-gonality: | $3 \le \gamma \le 5$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 21E5 |
Level structure
$\GL_2(\Z/273\Z)$-generators: | $\begin{bmatrix}78&19\\22&186\end{bmatrix}$, $\begin{bmatrix}85&114\\184&176\end{bmatrix}$, $\begin{bmatrix}237&70\\100&141\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 273.192.5.j.4 for the level structure with $-I$) |
Cyclic 273-isogeny field degree: | $14$ |
Cyclic 273-torsion field degree: | $2016$ |
Full 273-torsion field degree: | $6604416$ |
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 |
---|---|---|---|---|---|
21.128.1-21.a.4.4 | $21$ | $3$ | $3$ | $1$ | $0$ |
273.192.3-273.c.2.7 | $273$ | $2$ | $2$ | $3$ | $?$ |
273.192.3-273.c.2.16 | $273$ | $2$ | $2$ | $3$ | $?$ |