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 | $1^{4}\cdot2^{2}\cdot4^{2}\cdot16^{2}$ | 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: | 16H0 |
Level structure
$\GL_2(\Z/304\Z)$-generators: | $\begin{bmatrix}84&163\\133&106\end{bmatrix}$, $\begin{bmatrix}142&243\\61&228\end{bmatrix}$, $\begin{bmatrix}259&212\\302&297\end{bmatrix}$, $\begin{bmatrix}264&233\\9&240\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 304.48.0.bp.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.1.6 | $16$ | $2$ | $2$ | $0$ | $0$ |
152.48.0-8.bb.1.5 | $152$ | $2$ | $2$ | $0$ | $?$ |
304.48.0-304.f.1.9 | $304$ | $2$ | $2$ | $0$ | $?$ |
304.48.0-304.f.1.14 | $304$ | $2$ | $2$ | $0$ | $?$ |
304.48.0-304.h.1.10 | $304$ | $2$ | $2$ | $0$ | $?$ |
304.48.0-304.h.1.15 | $304$ | $2$ | $2$ | $0$ | $?$ |
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.f.2.3 | $304$ | $2$ | $2$ | $1$ |
304.192.1-304.ba.1.5 | $304$ | $2$ | $2$ | $1$ |
304.192.1-304.bm.2.4 | $304$ | $2$ | $2$ | $1$ |
304.192.1-304.by.1.3 | $304$ | $2$ | $2$ | $1$ |
304.192.1-304.cf.2.2 | $304$ | $2$ | $2$ | $1$ |
304.192.1-304.ct.1.5 | $304$ | $2$ | $2$ | $1$ |
304.192.1-304.cx.2.3 | $304$ | $2$ | $2$ | $1$ |
304.192.1-304.dh.2.3 | $304$ | $2$ | $2$ | $1$ |