Invariants
Level: | $304$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $2 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 14 }{2}$ | ||||||
Cusps: | $14$ (of which $2$ are rational) | Cusp widths | $4^{8}\cdot8^{4}\cdot16^{2}$ | Cusp orbits | $1^{2}\cdot2^{4}\cdot4$ | ||
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: | 16I2 |
Level structure
$\GL_2(\Z/304\Z)$-generators: | $\begin{bmatrix}81&44\\236&295\end{bmatrix}$, $\begin{bmatrix}129&244\\160&207\end{bmatrix}$, $\begin{bmatrix}169&192\\32&29\end{bmatrix}$, $\begin{bmatrix}177&208\\32&23\end{bmatrix}$, $\begin{bmatrix}201&12\\144&135\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 304.96.2.c.1 for the level structure with $-I$) |
Cyclic 304-isogeny field degree: | $80$ |
Cyclic 304-torsion field degree: | $2880$ |
Full 304-torsion field degree: | $15759360$ |
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 |
---|---|---|---|---|---|
8.96.0-8.c.1.1 | $8$ | $2$ | $2$ | $0$ | $0$ |
304.96.0-8.c.1.4 | $304$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
304.384.5-304.n.1.1 | $304$ | $2$ | $2$ | $5$ |
304.384.5-304.n.2.1 | $304$ | $2$ | $2$ | $5$ |
304.384.5-304.r.1.1 | $304$ | $2$ | $2$ | $5$ |
304.384.5-304.r.2.1 | $304$ | $2$ | $2$ | $5$ |
304.384.5-304.bl.1.1 | $304$ | $2$ | $2$ | $5$ |
304.384.5-304.bl.2.1 | $304$ | $2$ | $2$ | $5$ |
304.384.5-304.bn.1.1 | $304$ | $2$ | $2$ | $5$ |
304.384.5-304.bn.3.1 | $304$ | $2$ | $2$ | $5$ |
304.384.5-304.cw.1.1 | $304$ | $2$ | $2$ | $5$ |
304.384.5-304.cw.2.1 | $304$ | $2$ | $2$ | $5$ |
304.384.5-304.cx.1.5 | $304$ | $2$ | $2$ | $5$ |
304.384.5-304.cx.2.2 | $304$ | $2$ | $2$ | $5$ |
304.384.5-304.db.1.1 | $304$ | $2$ | $2$ | $5$ |
304.384.5-304.db.2.1 | $304$ | $2$ | $2$ | $5$ |
304.384.5-304.df.1.1 | $304$ | $2$ | $2$ | $5$ |
304.384.5-304.df.2.1 | $304$ | $2$ | $2$ | $5$ |
304.384.7-304.k.1.1 | $304$ | $2$ | $2$ | $7$ |
304.384.7-304.m.1.1 | $304$ | $2$ | $2$ | $7$ |
304.384.7-304.o.1.1 | $304$ | $2$ | $2$ | $7$ |
304.384.7-304.p.1.1 | $304$ | $2$ | $2$ | $7$ |
304.384.7-304.ba.1.1 | $304$ | $2$ | $2$ | $7$ |
304.384.7-304.bc.1.2 | $304$ | $2$ | $2$ | $7$ |
304.384.7-304.bg.1.1 | $304$ | $2$ | $2$ | $7$ |
304.384.7-304.bi.1.1 | $304$ | $2$ | $2$ | $7$ |