Invariants
| Level: | $276$ | $\SL_2$-level: | $12$ | ||||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
| Cusps: | $10$ (of which $2$ are rational) | Cusp widths | $1^{2}\cdot2\cdot3^{2}\cdot4^{2}\cdot6\cdot12^{2}$ | Cusp orbits | $1^{2}\cdot2^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 12J0 |
Level structure
| $\GL_2(\Z/276\Z)$-generators: | $\begin{bmatrix}44&19\\263&132\end{bmatrix}$, $\begin{bmatrix}98&67\\111&118\end{bmatrix}$, $\begin{bmatrix}238&153\\103&128\end{bmatrix}$, $\begin{bmatrix}246&91\\127&126\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 276.48.0.c.1 for the level structure with $-I$) |
| Cyclic 276-isogeny field degree: | $24$ |
| Cyclic 276-torsion field degree: | $2112$ |
| Full 276-torsion field degree: | $12824064$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 12.48.0-12.g.1.3 | $12$ | $2$ | $2$ | $0$ | $0$ |
| 276.48.0-12.g.1.2 | $276$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 276.192.1-276.b.3.4 | $276$ | $2$ | $2$ | $1$ |
| 276.192.1-276.i.2.5 | $276$ | $2$ | $2$ | $1$ |
| 276.192.1-276.j.1.6 | $276$ | $2$ | $2$ | $1$ |
| 276.192.1-276.k.1.2 | $276$ | $2$ | $2$ | $1$ |
| 276.192.1-276.l.1.2 | $276$ | $2$ | $2$ | $1$ |
| 276.192.1-276.m.1.4 | $276$ | $2$ | $2$ | $1$ |
| 276.192.1-276.n.2.6 | $276$ | $2$ | $2$ | $1$ |
| 276.192.1-276.o.4.3 | $276$ | $2$ | $2$ | $1$ |
| 276.288.3-276.c.1.9 | $276$ | $3$ | $3$ | $3$ |