Invariants
| Level: | $276$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (none of which are rational) | Cusp widths | $4^{6}\cdot12^{6}$ | Cusp orbits | $2^{6}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 12K3 |
Level structure
| $\GL_2(\Z/276\Z)$-generators: | $\begin{bmatrix}77&36\\10&85\end{bmatrix}$, $\begin{bmatrix}189&74\\256&103\end{bmatrix}$, $\begin{bmatrix}203&180\\66&17\end{bmatrix}$, $\begin{bmatrix}213&4\\274&261\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 276.96.3.i.1 for the level structure with $-I$) |
| Cyclic 276-isogeny field degree: | $48$ |
| Cyclic 276-torsion field degree: | $2112$ |
| Full 276-torsion field degree: | $6412032$ |
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 |
|---|---|---|---|---|---|
| 12.96.1-12.d.1.5 | $12$ | $2$ | $2$ | $1$ | $0$ |
| 276.48.0-276.f.1.8 | $276$ | $4$ | $4$ | $0$ | $?$ |
| 276.96.1-276.a.1.7 | $276$ | $2$ | $2$ | $1$ | $?$ |
| 276.96.1-276.a.1.8 | $276$ | $2$ | $2$ | $1$ | $?$ |
| 276.96.1-12.d.1.5 | $276$ | $2$ | $2$ | $1$ | $?$ |
| 276.96.1-276.d.1.1 | $276$ | $2$ | $2$ | $1$ | $?$ |
| 276.96.1-276.d.1.14 | $276$ | $2$ | $2$ | $1$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 276.384.5-276.n.1.6 | $276$ | $2$ | $2$ | $5$ |
| 276.384.5-276.n.2.7 | $276$ | $2$ | $2$ | $5$ |
| 276.384.5-276.n.3.1 | $276$ | $2$ | $2$ | $5$ |
| 276.384.5-276.n.4.1 | $276$ | $2$ | $2$ | $5$ |
| 276.384.5-276.x.1.3 | $276$ | $2$ | $2$ | $5$ |
| 276.384.5-276.x.2.3 | $276$ | $2$ | $2$ | $5$ |
| 276.384.5-276.x.3.5 | $276$ | $2$ | $2$ | $5$ |
| 276.384.5-276.x.4.5 | $276$ | $2$ | $2$ | $5$ |