Invariants
Level: | $276$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
Genus: | $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
Cusps: | $24$ (none of which are rational) | Cusp widths | $4^{12}\cdot12^{12}$ | Cusp orbits | $2^{4}\cdot4^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 8$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12E5 |
Level structure
$\GL_2(\Z/276\Z)$-generators: | $\begin{bmatrix}47&250\\92&9\end{bmatrix}$, $\begin{bmatrix}87&76\\26&163\end{bmatrix}$, $\begin{bmatrix}95&30\\14&265\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 276.192.5.g.1 for the level structure with $-I$) |
Cyclic 276-isogeny field degree: | $48$ |
Cyclic 276-torsion field degree: | $2112$ |
Full 276-torsion field degree: | $3206016$ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
12.192.1-12.a.2.6 | $12$ | $2$ | $2$ | $1$ | $0$ |
276.192.1-12.a.2.3 | $276$ | $2$ | $2$ | $1$ | $?$ |
276.192.1-276.f.2.3 | $276$ | $2$ | $2$ | $1$ | $?$ |
276.192.1-276.f.2.14 | $276$ | $2$ | $2$ | $1$ | $?$ |
276.192.1-276.f.4.2 | $276$ | $2$ | $2$ | $1$ | $?$ |
276.192.1-276.f.4.15 | $276$ | $2$ | $2$ | $1$ | $?$ |
276.192.3-276.b.1.3 | $276$ | $2$ | $2$ | $3$ | $?$ |
276.192.3-276.b.1.11 | $276$ | $2$ | $2$ | $3$ | $?$ |
276.192.3-276.k.1.7 | $276$ | $2$ | $2$ | $3$ | $?$ |
276.192.3-276.k.1.14 | $276$ | $2$ | $2$ | $3$ | $?$ |
276.192.3-276.p.1.6 | $276$ | $2$ | $2$ | $3$ | $?$ |
276.192.3-276.p.1.11 | $276$ | $2$ | $2$ | $3$ | $?$ |
276.192.3-276.p.1.14 | $276$ | $2$ | $2$ | $3$ | $?$ |