Invariants
Level: | $304$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $5 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (of which $2$ are rational) | Cusp widths | $8^{4}\cdot16^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $3 \le \gamma \le 5$ | ||||||
$\overline{\Q}$-gonality: | $3 \le \gamma \le 5$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16D5 |
Level structure
$\GL_2(\Z/304\Z)$-generators: | $\begin{bmatrix}37&226\\68&283\end{bmatrix}$, $\begin{bmatrix}89&190\\220&177\end{bmatrix}$, $\begin{bmatrix}131&174\\156&239\end{bmatrix}$, $\begin{bmatrix}237&284\\104&187\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 304.96.5.bk.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 |
---|---|---|---|---|---|
8.96.1-8.i.2.5 | $8$ | $2$ | $2$ | $1$ | $0$ |
304.96.1-8.i.2.3 | $304$ | $2$ | $2$ | $1$ | $?$ |
304.96.3-304.c.2.1 | $304$ | $2$ | $2$ | $3$ | $?$ |
304.96.3-304.c.2.21 | $304$ | $2$ | $2$ | $3$ | $?$ |
304.96.3-304.e.1.8 | $304$ | $2$ | $2$ | $3$ | $?$ |
304.96.3-304.e.1.22 | $304$ | $2$ | $2$ | $3$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
304.384.9-304.da.2.12 | $304$ | $2$ | $2$ | $9$ |
304.384.9-304.dh.2.1 | $304$ | $2$ | $2$ | $9$ |
304.384.9-304.dt.2.2 | $304$ | $2$ | $2$ | $9$ |
304.384.9-304.dw.1.7 | $304$ | $2$ | $2$ | $9$ |
304.384.9-304.fm.1.5 | $304$ | $2$ | $2$ | $9$ |
304.384.9-304.fp.2.6 | $304$ | $2$ | $2$ | $9$ |
304.384.9-304.ga.4.4 | $304$ | $2$ | $2$ | $9$ |
304.384.9-304.gj.1.14 | $304$ | $2$ | $2$ | $9$ |