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: | $10$ (of which $2$ are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot8^{4}$ | Cusp orbits | $1^{2}\cdot2^{2}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $1$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8O0 |
Level structure
$\GL_2(\Z/304\Z)$-generators: | $\begin{bmatrix}161&176\\182&85\end{bmatrix}$, $\begin{bmatrix}169&16\\221&173\end{bmatrix}$, $\begin{bmatrix}207&208\\5&137\end{bmatrix}$, $\begin{bmatrix}273&184\\186&191\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 152.48.0.bl.1 for the level structure with $-I$) |
Cyclic 304-isogeny field degree: | $40$ |
Cyclic 304-torsion field degree: | $2880$ |
Full 304-torsion field degree: | $31518720$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
16.48.0-8.bb.2.7 | $16$ | $2$ | $2$ | $0$ | $0$ |
304.48.0-8.bb.2.1 | $304$ | $2$ | $2$ | $0$ | $?$ |
304.48.0-152.bj.1.5 | $304$ | $2$ | $2$ | $0$ | $?$ |
304.48.0-152.bj.1.6 | $304$ | $2$ | $2$ | $0$ | $?$ |
304.48.0-152.bu.1.1 | $304$ | $2$ | $2$ | $0$ | $?$ |
304.48.0-152.bu.1.11 | $304$ | $2$ | $2$ | $0$ | $?$ |
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.cv.2.3 | $304$ | $2$ | $2$ | $1$ |
304.192.1-304.cx.1.5 | $304$ | $2$ | $2$ | $1$ |
304.192.1-304.dd.1.5 | $304$ | $2$ | $2$ | $1$ |
304.192.1-304.df.2.2 | $304$ | $2$ | $2$ | $1$ |
304.192.1-304.eb.1.9 | $304$ | $2$ | $2$ | $1$ |
304.192.1-304.ed.2.3 | $304$ | $2$ | $2$ | $1$ |
304.192.1-304.ej.2.5 | $304$ | $2$ | $2$ | $1$ |
304.192.1-304.el.1.5 | $304$ | $2$ | $2$ | $1$ |