Invariants
| Level: | $276$ | $\SL_2$-level: | $12$ | 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 | $4^{12}\cdot12^{12}$ | Cusp orbits | $2^{8}\cdot4^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 12E5 |
Level structure
| $\GL_2(\Z/276\Z)$-generators: | $\begin{bmatrix}1&162\\184&47\end{bmatrix}$, $\begin{bmatrix}35&58\\32&21\end{bmatrix}$, $\begin{bmatrix}231&224\\14&237\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 276.192.5.h.1 for the level structure with $-I$) |
| Cyclic 276-isogeny field degree: | $24$ |
| Cyclic 276-torsion field degree: | $1056$ |
| Full 276-torsion field degree: | $3206016$ |
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 |
|---|---|---|---|---|---|
| 12.192.1-12.b.4.2 | $12$ | $2$ | $2$ | $1$ | $0$ |
| 276.192.1-12.b.4.5 | $276$ | $2$ | $2$ | $1$ | $?$ |
| 276.192.1-276.e.2.8 | $276$ | $2$ | $2$ | $1$ | $?$ |
| 276.192.1-276.e.2.16 | $276$ | $2$ | $2$ | $1$ | $?$ |
| 276.192.1-276.f.4.8 | $276$ | $2$ | $2$ | $1$ | $?$ |
| 276.192.1-276.f.4.16 | $276$ | $2$ | $2$ | $1$ | $?$ |
| 276.192.3-276.c.1.13 | $276$ | $2$ | $2$ | $3$ | $?$ |
| 276.192.3-276.c.1.16 | $276$ | $2$ | $2$ | $3$ | $?$ |
| 276.192.3-276.l.1.5 | $276$ | $2$ | $2$ | $3$ | $?$ |
| 276.192.3-276.l.1.16 | $276$ | $2$ | $2$ | $3$ | $?$ |
| 276.192.3-276.o.1.7 | $276$ | $2$ | $2$ | $3$ | $?$ |
| 276.192.3-276.o.1.16 | $276$ | $2$ | $2$ | $3$ | $?$ |
| 276.192.3-276.p.1.14 | $276$ | $2$ | $2$ | $3$ | $?$ |
| 276.192.3-276.p.1.16 | $276$ | $2$ | $2$ | $3$ | $?$ |