Invariants
Level: | $204$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (of which $2$ are rational) | Cusp widths | $4^{6}\cdot12^{6}$ | Cusp orbits | $1^{2}\cdot2^{5}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 3$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12L3 |
Level structure
$\GL_2(\Z/204\Z)$-generators: | $\begin{bmatrix}29&40\\14&159\end{bmatrix}$, $\begin{bmatrix}37&74\\82&87\end{bmatrix}$, $\begin{bmatrix}119&138\\50&145\end{bmatrix}$, $\begin{bmatrix}131&108\\162&131\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 204.96.3.r.2 for the level structure with $-I$) |
Cyclic 204-isogeny field degree: | $36$ |
Cyclic 204-torsion field degree: | $1152$ |
Full 204-torsion field degree: | $1880064$ |
Rational points
This modular curve has 2 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 |
---|---|---|---|---|---|
12.96.0-12.a.2.9 | $12$ | $2$ | $2$ | $0$ | $0$ |
204.96.0-12.a.2.11 | $204$ | $2$ | $2$ | $0$ | $?$ |
204.96.1-204.d.1.3 | $204$ | $2$ | $2$ | $1$ | $?$ |
204.96.1-204.d.1.4 | $204$ | $2$ | $2$ | $1$ | $?$ |
204.96.2-204.a.2.5 | $204$ | $2$ | $2$ | $2$ | $?$ |
204.96.2-204.a.2.8 | $204$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
204.384.5-204.j.2.3 | $204$ | $2$ | $2$ | $5$ |
204.384.5-204.j.2.6 | $204$ | $2$ | $2$ | $5$ |
204.384.5-204.k.3.4 | $204$ | $2$ | $2$ | $5$ |
204.384.5-204.k.4.6 | $204$ | $2$ | $2$ | $5$ |
204.384.5-204.m.2.6 | $204$ | $2$ | $2$ | $5$ |
204.384.5-204.m.4.1 | $204$ | $2$ | $2$ | $5$ |
204.384.5-204.n.2.3 | $204$ | $2$ | $2$ | $5$ |
204.384.5-204.n.3.6 | $204$ | $2$ | $2$ | $5$ |