Invariants
Level: | $276$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{4}\cdot6^{4}\cdot12^{4}$ | Cusp orbits | $2^{6}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12V1 |
Level structure
$\GL_2(\Z/276\Z)$-generators: | $\begin{bmatrix}95&12\\120&139\end{bmatrix}$, $\begin{bmatrix}119&84\\158&49\end{bmatrix}$, $\begin{bmatrix}133&180\\248&191\end{bmatrix}$, $\begin{bmatrix}199&198\\234&43\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 276.96.1.e.2 for the level structure with $-I$) |
Cyclic 276-isogeny field degree: | $48$ |
Cyclic 276-torsion field degree: | $2112$ |
Full 276-torsion field degree: | $6412032$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
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 | Kernel decomposition |
---|---|---|---|---|---|---|
12.96.0-12.a.2.9 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
276.96.0-12.a.2.7 | $276$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
276.96.0-276.a.1.9 | $276$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
276.96.0-276.a.1.27 | $276$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
276.96.1-276.a.1.5 | $276$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
276.96.1-276.a.1.14 | $276$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
276.384.5-276.f.2.2 | $276$ | $2$ | $2$ | $5$ | $?$ | not computed |
276.384.5-276.h.1.8 | $276$ | $2$ | $2$ | $5$ | $?$ | not computed |
276.384.5-276.l.1.3 | $276$ | $2$ | $2$ | $5$ | $?$ | not computed |
276.384.5-276.n.3.6 | $276$ | $2$ | $2$ | $5$ | $?$ | not computed |
276.384.5-276.p.1.4 | $276$ | $2$ | $2$ | $5$ | $?$ | not computed |
276.384.5-276.r.3.5 | $276$ | $2$ | $2$ | $5$ | $?$ | not computed |
276.384.5-276.v.3.4 | $276$ | $2$ | $2$ | $5$ | $?$ | not computed |
276.384.5-276.x.3.7 | $276$ | $2$ | $2$ | $5$ | $?$ | not computed |