Invariants
| Level: | $204$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $2 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (all of which are rational) | Cusp widths | $4^{3}\cdot12^{3}$ | Cusp orbits | $1^{6}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $6$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 12F2 |
Level structure
| $\GL_2(\Z/204\Z)$-generators: | $\begin{bmatrix}11&178\\12&7\end{bmatrix}$, $\begin{bmatrix}119&76\\174&199\end{bmatrix}$, $\begin{bmatrix}143&160\\18&97\end{bmatrix}$, $\begin{bmatrix}155&78\\146&31\end{bmatrix}$, $\begin{bmatrix}181&54\\180&31\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 204.48.2.a.2 for the level structure with $-I$) |
| Cyclic 204-isogeny field degree: | $36$ |
| Cyclic 204-torsion field degree: | $2304$ |
| Full 204-torsion field degree: | $3760128$ |
Rational points
This modular curve has 6 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 12.48.0-6.a.1.6 | $12$ | $2$ | $2$ | $0$ | $0$ |
| 204.48.0-6.a.1.8 | $204$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 204.192.3-204.k.2.4 | $204$ | $2$ | $2$ | $3$ |
| 204.192.3-204.k.2.13 | $204$ | $2$ | $2$ | $3$ |
| 204.192.3-204.l.2.3 | $204$ | $2$ | $2$ | $3$ |
| 204.192.3-204.l.2.6 | $204$ | $2$ | $2$ | $3$ |
| 204.192.3-204.l.2.12 | $204$ | $2$ | $2$ | $3$ |
| 204.192.3-204.m.2.2 | $204$ | $2$ | $2$ | $3$ |
| 204.192.3-204.m.2.6 | $204$ | $2$ | $2$ | $3$ |
| 204.192.3-204.m.2.15 | $204$ | $2$ | $2$ | $3$ |
| 204.192.3-204.n.2.2 | $204$ | $2$ | $2$ | $3$ |
| 204.192.3-204.n.2.8 | $204$ | $2$ | $2$ | $3$ |
| 204.192.3-204.n.2.11 | $204$ | $2$ | $2$ | $3$ |
| 204.192.3-204.o.2.3 | $204$ | $2$ | $2$ | $3$ |
| 204.192.3-204.o.2.5 | $204$ | $2$ | $2$ | $3$ |
| 204.192.3-204.o.2.16 | $204$ | $2$ | $2$ | $3$ |
| 204.192.3-204.p.2.4 | $204$ | $2$ | $2$ | $3$ |
| 204.192.3-204.p.2.8 | $204$ | $2$ | $2$ | $3$ |
| 204.192.3-204.p.2.9 | $204$ | $2$ | $2$ | $3$ |
| 204.192.3-204.q.2.2 | $204$ | $2$ | $2$ | $3$ |
| 204.192.3-204.q.2.6 | $204$ | $2$ | $2$ | $3$ |
| 204.192.3-204.q.2.15 | $204$ | $2$ | $2$ | $3$ |
| 204.192.3-204.r.2.4 | $204$ | $2$ | $2$ | $3$ |
| 204.192.3-204.r.2.6 | $204$ | $2$ | $2$ | $3$ |
| 204.192.3-204.r.2.11 | $204$ | $2$ | $2$ | $3$ |
| 204.288.7-204.o.1.10 | $204$ | $3$ | $3$ | $7$ |