Invariants
Level: | $204$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (of which $2$ are rational) | Cusp widths | $2^{4}\cdot4^{4}\cdot6^{4}\cdot12^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}\cdot4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12V1 |
Level structure
$\GL_2(\Z/204\Z)$-generators: | $\begin{bmatrix}67&156\\101&163\end{bmatrix}$, $\begin{bmatrix}73&84\\167&155\end{bmatrix}$, $\begin{bmatrix}85&144\\138&91\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 204.96.1.l.1 for the level structure with $-I$) |
Cyclic 204-isogeny field degree: | $18$ |
Cyclic 204-torsion field degree: | $1152$ |
Full 204-torsion field degree: | $1880064$ |
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 |
---|---|---|---|---|---|---|
12.96.0-12.c.3.3 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
204.96.0-12.c.3.5 | $204$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
204.96.0-204.c.4.7 | $204$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
204.96.0-204.c.4.16 | $204$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
204.96.1-204.k.1.4 | $204$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
204.96.1-204.k.1.12 | $204$ | $2$ | $2$ | $1$ | $?$ | dimension zero |