Invariants
Level: | $304$ | $\SL_2$-level: | $16$ | ||||
Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $1^{2}\cdot2\cdot4\cdot8^{2}$ | Cusp orbits | $1^{2}\cdot2^{2}$ | ||
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: | 8I0 |
Level structure
$\GL_2(\Z/304\Z)$-generators: | $\begin{bmatrix}84&45\\85&164\end{bmatrix}$, $\begin{bmatrix}102&107\\113&256\end{bmatrix}$, $\begin{bmatrix}129&144\\140&133\end{bmatrix}$, $\begin{bmatrix}160&171\\37&206\end{bmatrix}$, $\begin{bmatrix}290&221\\41&214\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 152.24.0.bu.1 for the level structure with $-I$) |
Cyclic 304-isogeny field degree: | $40$ |
Cyclic 304-torsion field degree: | $2880$ |
Full 304-torsion field degree: | $63037440$ |
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 |
---|---|---|---|---|---|
16.24.0-8.n.1.8 | $16$ | $2$ | $2$ | $0$ | $0$ |
304.24.0-8.n.1.2 | $304$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
304.96.0-152.z.1.4 | $304$ | $2$ | $2$ | $0$ |
304.96.0-152.bc.2.3 | $304$ | $2$ | $2$ | $0$ |
304.96.0-152.bd.1.4 | $304$ | $2$ | $2$ | $0$ |
304.96.0-152.be.1.2 | $304$ | $2$ | $2$ | $0$ |
304.96.0-152.bg.1.8 | $304$ | $2$ | $2$ | $0$ |
304.96.0-152.bj.1.6 | $304$ | $2$ | $2$ | $0$ |
304.96.0-152.bl.1.4 | $304$ | $2$ | $2$ | $0$ |
304.96.0-152.bm.1.3 | $304$ | $2$ | $2$ | $0$ |
304.96.0-304.bc.2.2 | $304$ | $2$ | $2$ | $0$ |
304.96.0-304.bi.2.5 | $304$ | $2$ | $2$ | $0$ |
304.96.0-304.bk.1.5 | $304$ | $2$ | $2$ | $0$ |
304.96.0-304.bq.1.2 | $304$ | $2$ | $2$ | $0$ |
304.96.0-304.bs.2.2 | $304$ | $2$ | $2$ | $0$ |
304.96.0-304.bu.2.5 | $304$ | $2$ | $2$ | $0$ |
304.96.0-304.bw.1.5 | $304$ | $2$ | $2$ | $0$ |
304.96.0-304.by.1.2 | $304$ | $2$ | $2$ | $0$ |
304.96.1-304.bg.1.2 | $304$ | $2$ | $2$ | $1$ |
304.96.1-304.bi.1.5 | $304$ | $2$ | $2$ | $1$ |
304.96.1-304.bk.2.5 | $304$ | $2$ | $2$ | $1$ |
304.96.1-304.bm.2.2 | $304$ | $2$ | $2$ | $1$ |
304.96.1-304.bo.1.2 | $304$ | $2$ | $2$ | $1$ |
304.96.1-304.bu.1.5 | $304$ | $2$ | $2$ | $1$ |
304.96.1-304.bw.2.5 | $304$ | $2$ | $2$ | $1$ |
304.96.1-304.cc.2.2 | $304$ | $2$ | $2$ | $1$ |