Invariants
Level: | $276$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $24$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (all of which are rational) | Cusp widths | $2\cdot4\cdot6\cdot12$ | Cusp orbits | $1^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12F1 |
Level structure
$\GL_2(\Z/276\Z)$-generators: | $\begin{bmatrix}131&244\\14&201\end{bmatrix}$, $\begin{bmatrix}209&186\\228&35\end{bmatrix}$, $\begin{bmatrix}245&42\\236&73\end{bmatrix}$, $\begin{bmatrix}248&27\\177&152\end{bmatrix}$, $\begin{bmatrix}271&236\\208&81\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 276.48.1-276.p.1.1, 276.48.1-276.p.1.2, 276.48.1-276.p.1.3, 276.48.1-276.p.1.4, 276.48.1-276.p.1.5, 276.48.1-276.p.1.6, 276.48.1-276.p.1.7, 276.48.1-276.p.1.8, 276.48.1-276.p.1.9, 276.48.1-276.p.1.10, 276.48.1-276.p.1.11, 276.48.1-276.p.1.12, 276.48.1-276.p.1.13, 276.48.1-276.p.1.14, 276.48.1-276.p.1.15, 276.48.1-276.p.1.16 |
Cyclic 276-isogeny field degree: | $48$ |
Cyclic 276-torsion field degree: | $4224$ |
Full 276-torsion field degree: | $51296256$ |
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
The following modular covers realize this modular curve as a fiber product over $X(1)$.
Factor curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
$X_0(3)$ | $3$ | $6$ | $6$ | $0$ | $0$ | full Jacobian |
92.6.0.e.1 | $92$ | $4$ | $4$ | $0$ | $?$ | full Jacobian |
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
$X_0(6)$ | $6$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
92.6.0.e.1 | $92$ | $4$ | $4$ | $0$ | $?$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
276.48.1.a.1 | $276$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
276.48.1.h.1 | $276$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
276.48.1.i.1 | $276$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
276.48.1.l.1 | $276$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
276.48.1.z.1 | $276$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
276.48.1.bb.1 | $276$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
276.48.1.bd.1 | $276$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
276.48.1.bf.1 | $276$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
276.72.3.mb.1 | $276$ | $3$ | $3$ | $3$ | $?$ | not computed |