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: | $8$ (of which $4$ are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot6^{2}\cdot12^{2}$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12P1 |
Level structure
$\GL_2(\Z/204\Z)$-generators: | $\begin{bmatrix}91&69\\148&185\end{bmatrix}$, $\begin{bmatrix}133&59\\100&183\end{bmatrix}$, $\begin{bmatrix}157&179\\156&161\end{bmatrix}$, $\begin{bmatrix}181&98\\148&45\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 204.48.1.k.1 for the level structure with $-I$) |
Cyclic 204-isogeny field degree: | $18$ |
Cyclic 204-torsion field degree: | $1152$ |
Full 204-torsion field degree: | $3760128$ |
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 |
---|---|---|---|---|---|---|
12.48.0-12.g.1.3 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
204.24.0-68.g.1.1 | $204$ | $4$ | $4$ | $0$ | $?$ | full Jacobian |
204.48.0-12.g.1.3 | $204$ | $2$ | $2$ | $0$ | $?$ | 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 |
---|---|---|---|---|---|---|
204.192.1-204.l.1.2 | $204$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
204.192.1-204.l.1.3 | $204$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
204.192.1-204.l.2.1 | $204$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
204.192.1-204.l.2.4 | $204$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
204.192.1-204.l.3.2 | $204$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
204.192.1-204.l.3.5 | $204$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
204.192.1-204.l.4.1 | $204$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
204.192.1-204.l.4.6 | $204$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
204.288.5-204.ca.1.4 | $204$ | $3$ | $3$ | $5$ | $?$ | not computed |