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: | $\begin{bmatrix}121&192\\68&233\end{bmatrix}$, $\begin{bmatrix}233&76\\32&89\end{bmatrix}$, $\begin{bmatrix}233&168\\168&267\end{bmatrix}$, $\begin{bmatrix}295&20\\128&225\end{bmatrix}$, $\begin{bmatrix}295&248\\0&17\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 304.96.2.d.1 for the level structure with $-I$) |
Cyclic 304-isogeny field degree: | $80$ |
Cyclic 304-torsion field degree: | $5760$ |
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.1.5 | $8$ | $2$ | $2$ | $0$ | $0$ |
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.p.1.3 | $304$ | $2$ | $2$ | $5$ |
304.384.5-304.p.2.2 | $304$ | $2$ | $2$ | $5$ |
304.384.5-304.t.1.3 | $304$ | $2$ | $2$ | $5$ |
304.384.5-304.t.2.2 | $304$ | $2$ | $2$ | $5$ |
304.384.5-304.bo.1.5 | $304$ | $2$ | $2$ | $5$ |
304.384.5-304.bo.4.3 | $304$ | $2$ | $2$ | $5$ |
304.384.5-304.bs.1.3 | $304$ | $2$ | $2$ | $5$ |
304.384.5-304.bs.2.3 | $304$ | $2$ | $2$ | $5$ |
304.384.5-304.cx.1.2 | $304$ | $2$ | $2$ | $5$ |
304.384.5-304.cx.2.5 | $304$ | $2$ | $2$ | $5$ |
304.384.5-304.cz.1.5 | $304$ | $2$ | $2$ | $5$ |
304.384.5-304.cz.2.2 | $304$ | $2$ | $2$ | $5$ |
304.384.5-304.dd.1.5 | $304$ | $2$ | $2$ | $5$ |
304.384.5-304.dd.2.3 | $304$ | $2$ | $2$ | $5$ |
304.384.5-304.dh.1.2 | $304$ | $2$ | $2$ | $5$ |
304.384.5-304.dh.2.2 | $304$ | $2$ | $2$ | $5$ |
304.384.7-304.l.1.5 | $304$ | $2$ | $2$ | $7$ |
304.384.7-304.n.1.9 | $304$ | $2$ | $2$ | $7$ |
304.384.7-304.q.1.9 | $304$ | $2$ | $2$ | $7$ |
304.384.7-304.t.1.9 | $304$ | $2$ | $2$ | $7$ |
304.384.7-304.bc.1.5 | $304$ | $2$ | $2$ | $7$ |
304.384.7-304.bd.1.5 | $304$ | $2$ | $2$ | $7$ |
304.384.7-304.bh.1.5 | $304$ | $2$ | $2$ | $7$ |
304.384.7-304.bj.1.5 | $304$ | $2$ | $2$ | $7$ |