Invariants
Level: | $304$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (all of which are rational) | Cusp widths | $2^{2}\cdot4\cdot16$ | Cusp orbits | $1^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16A1 |
Level structure
$\GL_2(\Z/304\Z)$-generators: | $\begin{bmatrix}21&204\\272&57\end{bmatrix}$, $\begin{bmatrix}42&165\\283&216\end{bmatrix}$, $\begin{bmatrix}72&103\\49&106\end{bmatrix}$, $\begin{bmatrix}206&93\\143&16\end{bmatrix}$, $\begin{bmatrix}288&89\\37&276\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 304.24.1.b.1 for the level structure with $-I$) |
Cyclic 304-isogeny field degree: | $40$ |
Cyclic 304-torsion field degree: | $5760$ |
Full 304-torsion field degree: | $63037440$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
8.24.0-8.n.1.6 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
304.24.0-8.n.1.7 | $304$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
304.96.1-304.b.2.2 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.f.1.4 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.h.1.2 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.j.1.4 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.bw.1.14 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.bw.2.10 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.bx.1.14 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.bx.2.10 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.by.1.15 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.by.2.11 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.bz.1.14 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.bz.2.11 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.ca.1.13 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.ca.2.14 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.cb.1.13 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.cb.2.15 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.cc.1.13 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.cc.2.12 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.cd.1.13 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.cd.2.12 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.ce.1.2 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.ch.1.4 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.ci.1.2 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.96.1-304.cl.1.4 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |