Invariants
Level: | $204$ | $\SL_2$-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
$\GL_2(\Z/204\Z)$-generators: | $\begin{bmatrix}139&134\\190&87\end{bmatrix}$, $\begin{bmatrix}149&141\\14&187\end{bmatrix}$, $\begin{bmatrix}195&142\\176&61\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 204.48.1.z.1 for the level structure with $-I$) |
Cyclic 204-isogeny field degree: | $36$ |
Cyclic 204-torsion field degree: | $2304$ |
Full 204-torsion field degree: | $3760128$ |
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 |
---|---|---|---|---|---|---|
12.48.0-6.b.1.2 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
102.48.0-6.b.1.1 | $102$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
204.48.0-204.s.1.11 | $204$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
204.48.0-204.s.1.14 | $204$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
204.48.1-204.p.1.11 | $204$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
204.48.1-204.p.1.14 | $204$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
204.288.5-204.ge.1.3 | $204$ | $3$ | $3$ | $5$ | $?$ | not computed |