Invariants
Level: | $276$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (of which $2$ are rational) | Cusp widths | $2^{4}\cdot4^{4}\cdot6^{4}\cdot12^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}\cdot4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12V1 |
Level structure
$\GL_2(\Z/276\Z)$-generators: | $\begin{bmatrix}31&12\\231&115\end{bmatrix}$, $\begin{bmatrix}43&216\\130&167\end{bmatrix}$, $\begin{bmatrix}77&180\\108&175\end{bmatrix}$, $\begin{bmatrix}181&228\\145&11\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 276.192.1-276.m.1.1, 276.192.1-276.m.1.2, 276.192.1-276.m.1.3, 276.192.1-276.m.1.4, 276.192.1-276.m.1.5, 276.192.1-276.m.1.6, 276.192.1-276.m.1.7, 276.192.1-276.m.1.8 |
Cyclic 276-isogeny field degree: | $24$ |
Cyclic 276-torsion field degree: | $2112$ |
Full 276-torsion field degree: | $12824064$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
12.48.0.c.3 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
276.48.0.c.1 | $276$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
276.48.1.l.1 | $276$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
276.288.9.l.1 | $276$ | $3$ | $3$ | $9$ | $?$ | not computed |