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 | $1^{2}\cdot2^{3}\cdot16$ | 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: | 16D0 |
Level structure
$\GL_2(\Z/304\Z)$-generators: | $\begin{bmatrix}16&73\\205&68\end{bmatrix}$, $\begin{bmatrix}28&131\\95&176\end{bmatrix}$, $\begin{bmatrix}40&259\\1&146\end{bmatrix}$, $\begin{bmatrix}115&242\\124&65\end{bmatrix}$, $\begin{bmatrix}240&143\\221&250\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 304.24.0.f.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 | $16$ | $2$ | $2$ | $0$ | $0$ |
152.24.0-8.n.1.3 | $152$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
304.96.0-304.d.2.9 | $304$ | $2$ | $2$ | $0$ |
304.96.0-304.f.1.11 | $304$ | $2$ | $2$ | $0$ |
304.96.0-304.k.1.18 | $304$ | $2$ | $2$ | $0$ |
304.96.0-304.l.1.9 | $304$ | $2$ | $2$ | $0$ |
304.96.0-304.u.2.5 | $304$ | $2$ | $2$ | $0$ |
304.96.0-304.x.1.11 | $304$ | $2$ | $2$ | $0$ |
304.96.0-304.z.2.13 | $304$ | $2$ | $2$ | $0$ |
304.96.0-304.ba.1.9 | $304$ | $2$ | $2$ | $0$ |
304.96.0-304.bg.2.5 | $304$ | $2$ | $2$ | $0$ |
304.96.0-304.bh.2.1 | $304$ | $2$ | $2$ | $0$ |
304.96.0-304.bo.2.1 | $304$ | $2$ | $2$ | $0$ |
304.96.0-304.bp.1.5 | $304$ | $2$ | $2$ | $0$ |
304.96.0-304.bu.2.5 | $304$ | $2$ | $2$ | $0$ |
304.96.0-304.bv.2.1 | $304$ | $2$ | $2$ | $0$ |
304.96.0-304.by.2.1 | $304$ | $2$ | $2$ | $0$ |
304.96.0-304.bz.1.5 | $304$ | $2$ | $2$ | $0$ |
304.96.1-304.bi.2.5 | $304$ | $2$ | $2$ | $1$ |
304.96.1-304.bj.2.1 | $304$ | $2$ | $2$ | $1$ |
304.96.1-304.bm.2.1 | $304$ | $2$ | $2$ | $1$ |
304.96.1-304.bn.2.5 | $304$ | $2$ | $2$ | $1$ |
304.96.1-304.bs.2.5 | $304$ | $2$ | $2$ | $1$ |
304.96.1-304.bt.2.1 | $304$ | $2$ | $2$ | $1$ |
304.96.1-304.ca.2.1 | $304$ | $2$ | $2$ | $1$ |
304.96.1-304.cb.2.5 | $304$ | $2$ | $2$ | $1$ |