Invariants
| Level: | $276$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $2 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (all of which are rational) | Cusp widths | $4^{3}\cdot12^{3}$ | Cusp orbits | $1^{6}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $6$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 12F2 |
Level structure
| $\GL_2(\Z/276\Z)$-generators: | $\begin{bmatrix}23&232\\206&171\end{bmatrix}$, $\begin{bmatrix}47&88\\198&133\end{bmatrix}$, $\begin{bmatrix}101&18\\32&253\end{bmatrix}$, $\begin{bmatrix}105&188\\182&129\end{bmatrix}$, $\begin{bmatrix}251&208\\114&271\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 276.48.2.a.1 for the level structure with $-I$) |
| Cyclic 276-isogeny field degree: | $48$ |
| Cyclic 276-torsion field degree: | $2112$ |
| Full 276-torsion field degree: | $12824064$ |
Rational points
This modular curve has 6 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 12.48.0-6.a.1.3 | $12$ | $2$ | $2$ | $0$ | $0$ |
| 276.48.0-6.a.1.6 | $276$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 276.192.3-276.k.1.3 | $276$ | $2$ | $2$ | $3$ |
| 276.192.3-276.k.1.14 | $276$ | $2$ | $2$ | $3$ |
| 276.192.3-276.l.1.3 | $276$ | $2$ | $2$ | $3$ |
| 276.192.3-276.l.1.13 | $276$ | $2$ | $2$ | $3$ |
| 276.192.3-276.l.1.16 | $276$ | $2$ | $2$ | $3$ |
| 276.192.3-276.m.1.6 | $276$ | $2$ | $2$ | $3$ |
| 276.192.3-276.m.1.11 | $276$ | $2$ | $2$ | $3$ |
| 276.192.3-276.m.1.14 | $276$ | $2$ | $2$ | $3$ |
| 276.192.3-276.n.1.7 | $276$ | $2$ | $2$ | $3$ |
| 276.192.3-276.n.1.12 | $276$ | $2$ | $2$ | $3$ |
| 276.192.3-276.n.1.13 | $276$ | $2$ | $2$ | $3$ |
| 276.192.3-276.o.1.7 | $276$ | $2$ | $2$ | $3$ |
| 276.192.3-276.o.1.11 | $276$ | $2$ | $2$ | $3$ |
| 276.192.3-276.o.1.14 | $276$ | $2$ | $2$ | $3$ |
| 276.192.3-276.p.1.6 | $276$ | $2$ | $2$ | $3$ |
| 276.192.3-276.p.1.11 | $276$ | $2$ | $2$ | $3$ |
| 276.192.3-276.p.1.14 | $276$ | $2$ | $2$ | $3$ |
| 276.192.3-276.q.1.6 | $276$ | $2$ | $2$ | $3$ |
| 276.192.3-276.q.1.11 | $276$ | $2$ | $2$ | $3$ |
| 276.192.3-276.q.1.15 | $276$ | $2$ | $2$ | $3$ |
| 276.192.3-276.r.1.2 | $276$ | $2$ | $2$ | $3$ |
| 276.192.3-276.r.1.14 | $276$ | $2$ | $2$ | $3$ |
| 276.192.3-276.r.1.15 | $276$ | $2$ | $2$ | $3$ |
| 276.288.7-276.o.1.7 | $276$ | $3$ | $3$ | $7$ |