Invariants
| Level: | $276$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
| Index: | $96$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (of which $2$ are rational) | Cusp widths | $4^{6}\cdot12^{6}$ | Cusp orbits | $1^{2}\cdot2^{5}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 3$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 12L3 |
Level structure
| $\GL_2(\Z/276\Z)$-generators: | $\begin{bmatrix}11&126\\134&127\end{bmatrix}$, $\begin{bmatrix}29&10\\66&247\end{bmatrix}$, $\begin{bmatrix}133&44\\204&233\end{bmatrix}$, $\begin{bmatrix}135&62\\4&107\end{bmatrix}$, $\begin{bmatrix}183&26\\214&29\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | 276.192.3-276.p.1.1, 276.192.3-276.p.1.2, 276.192.3-276.p.1.3, 276.192.3-276.p.1.4, 276.192.3-276.p.1.5, 276.192.3-276.p.1.6, 276.192.3-276.p.1.7, 276.192.3-276.p.1.8, 276.192.3-276.p.1.9, 276.192.3-276.p.1.10, 276.192.3-276.p.1.11, 276.192.3-276.p.1.12, 276.192.3-276.p.1.13, 276.192.3-276.p.1.14, 276.192.3-276.p.1.15, 276.192.3-276.p.1.16 |
| Cyclic 276-isogeny field degree: | $48$ |
| Cyclic 276-torsion field degree: | $4224$ |
| Full 276-torsion field degree: | $12824064$ |
Rational points
This modular curve has 2 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.a.2 | $12$ | $2$ | $2$ | $0$ | $0$ |
| 276.48.1.b.1 | $276$ | $2$ | $2$ | $1$ | $?$ |
| 276.48.2.a.1 | $276$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 276.192.5.g.1 | $276$ | $2$ | $2$ | $5$ |
| 276.192.5.h.1 | $276$ | $2$ | $2$ | $5$ |
| 276.192.5.h.3 | $276$ | $2$ | $2$ | $5$ |
| 276.192.5.m.1 | $276$ | $2$ | $2$ | $5$ |
| 276.192.5.m.4 | $276$ | $2$ | $2$ | $5$ |
| 276.192.5.o.1 | $276$ | $2$ | $2$ | $5$ |
| 276.192.5.o.2 | $276$ | $2$ | $2$ | $5$ |
| 276.288.13.p.1 | $276$ | $3$ | $3$ | $13$ |