Invariants
Level: | $276$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot6^{2}\cdot12^{2}$ | Cusp orbits | $2^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 48$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12P1 |
Level structure
$\GL_2(\Z/276\Z)$-generators: | $\begin{bmatrix}121&236\\36&89\end{bmatrix}$, $\begin{bmatrix}139&42\\66&85\end{bmatrix}$, $\begin{bmatrix}167&88\\194&237\end{bmatrix}$, $\begin{bmatrix}223&129\\204&253\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 276.48.1.bu.1 for the level structure with $-I$) |
Cyclic 276-isogeny field degree: | $48$ |
Cyclic 276-torsion field degree: | $4224$ |
Full 276-torsion field degree: | $12824064$ |
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 |
---|---|---|---|---|---|---|
12.48.1-12.l.1.10 | $12$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
138.48.0-138.b.1.3 | $138$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
276.48.0-138.b.1.4 | $276$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
276.48.0-276.q.1.2 | $276$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
276.48.0-276.q.1.7 | $276$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
276.48.1-12.l.1.11 | $276$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
276.192.3-276.bw.1.8 | $276$ | $2$ | $2$ | $3$ | $?$ | not computed |
276.192.3-276.bx.1.4 | $276$ | $2$ | $2$ | $3$ | $?$ | not computed |
276.192.3-276.by.1.8 | $276$ | $2$ | $2$ | $3$ | $?$ | not computed |
276.192.3-276.bz.1.4 | $276$ | $2$ | $2$ | $3$ | $?$ | not computed |
276.288.5-276.gz.1.1 | $276$ | $3$ | $3$ | $5$ | $?$ | not computed |