Invariants
Level: | $204$ | $\SL_2$-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
$\GL_2(\Z/204\Z)$-generators: | $\begin{bmatrix}61&152\\60&83\end{bmatrix}$, $\begin{bmatrix}106&45\\73&44\end{bmatrix}$, $\begin{bmatrix}151&198\\198&73\end{bmatrix}$, $\begin{bmatrix}174&175\\115&90\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 204.24.1.o.1 for the level structure with $-I$) |
Cyclic 204-isogeny field degree: | $36$ |
Cyclic 204-torsion field degree: | $2304$ |
Full 204-torsion field degree: | $7520256$ |
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 |
204.24.0-6.a.1.2 | $204$ | $2$ | $2$ | $0$ | $?$ | 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 |
---|---|---|---|---|---|---|
204.96.1-204.b.1.11 | $204$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
204.96.1-204.e.1.11 | $204$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
204.96.1-204.j.1.1 | $204$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
204.96.1-204.k.1.5 | $204$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
204.96.1-204.y.1.2 | $204$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
204.96.1-204.ba.1.3 | $204$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
204.96.1-204.bc.1.5 | $204$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
204.96.1-204.be.1.1 | $204$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
204.144.3-204.ma.1.7 | $204$ | $3$ | $3$ | $3$ | $?$ | not computed |