Invariants
Level: | $304$ | $\SL_2$-level: | $16$ | ||||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (none of which are rational) | Cusp widths | $1^{4}\cdot2^{2}\cdot4^{2}\cdot16^{2}$ | Cusp orbits | $2^{5}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16H0 |
Level structure
$\GL_2(\Z/304\Z)$-generators: | $\begin{bmatrix}2&287\\299&214\end{bmatrix}$, $\begin{bmatrix}143&286\\246&103\end{bmatrix}$, $\begin{bmatrix}194&55\\173&268\end{bmatrix}$, $\begin{bmatrix}211&258\\238&167\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 304.48.0.bt.2 for the level structure with $-I$) |
Cyclic 304-isogeny field degree: | $20$ |
Cyclic 304-torsion field degree: | $1440$ |
Full 304-torsion field degree: | $31518720$ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
16.48.0-16.g.1.2 | $16$ | $2$ | $2$ | $0$ | $0$ |
152.48.0-152.bv.2.7 | $152$ | $2$ | $2$ | $0$ | $?$ |
304.48.0-304.e.2.9 | $304$ | $2$ | $2$ | $0$ | $?$ |
304.48.0-304.e.2.12 | $304$ | $2$ | $2$ | $0$ | $?$ |
304.48.0-16.g.1.10 | $304$ | $2$ | $2$ | $0$ | $?$ |
304.48.0-152.bv.2.1 | $304$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
304.192.1-304.l.2.5 | $304$ | $2$ | $2$ | $1$ |
304.192.1-304.s.1.3 | $304$ | $2$ | $2$ | $1$ |
304.192.1-304.bk.1.5 | $304$ | $2$ | $2$ | $1$ |
304.192.1-304.bs.1.3 | $304$ | $2$ | $2$ | $1$ |
304.192.1-304.dn.1.5 | $304$ | $2$ | $2$ | $1$ |
304.192.1-304.do.2.3 | $304$ | $2$ | $2$ | $1$ |
304.192.1-304.ea.1.5 | $304$ | $2$ | $2$ | $1$ |
304.192.1-304.eh.2.3 | $304$ | $2$ | $2$ | $1$ |