Invariants
Level: | $276$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $48$ | $\PSL_2$-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: | $\begin{bmatrix}141&76\\266&25\end{bmatrix}$, $\begin{bmatrix}141&116\\74&273\end{bmatrix}$, $\begin{bmatrix}220&243\\51&16\end{bmatrix}$, $\begin{bmatrix}259&218\\186&137\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 276.24.1.m.1 for the level structure with $-I$) |
Cyclic 276-isogeny field degree: | $48$ |
Cyclic 276-torsion field degree: | $4224$ |
Full 276-torsion field degree: | $25648128$ |
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 |
---|---|---|---|---|---|---|
12.24.0-6.a.1.6 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
276.24.0-6.a.1.3 | $276$ | $2$ | $2$ | $0$ | $?$ | 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 |
---|---|---|---|---|---|---|
276.96.1-276.d.1.13 | $276$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
276.96.1-276.f.1.3 | $276$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
276.96.1-276.n.1.1 | $276$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
276.96.1-276.o.1.2 | $276$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
276.96.1-276.r.1.3 | $276$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
276.96.1-276.s.1.5 | $276$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
276.96.1-276.v.1.5 | $276$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
276.96.1-276.w.1.3 | $276$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
276.144.3-276.jx.1.7 | $276$ | $3$ | $3$ | $3$ | $?$ | not computed |