Invariants
Level: | $304$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (of which $2$ are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot16^{2}$ | Cusp orbits | $1^{2}\cdot2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16E1 |
Level structure
$\GL_2(\Z/304\Z)$-generators: | $\begin{bmatrix}3&240\\186&181\end{bmatrix}$, $\begin{bmatrix}29&296\\124&251\end{bmatrix}$, $\begin{bmatrix}175&112\\274&105\end{bmatrix}$, $\begin{bmatrix}275&104\\164&103\end{bmatrix}$, $\begin{bmatrix}281&8\\210&127\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 304.48.1.b.2 for the level structure with $-I$) |
Cyclic 304-isogeny field degree: | $40$ |
Cyclic 304-torsion field degree: | $2880$ |
Full 304-torsion field degree: | $31518720$ |
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 |
---|---|---|---|---|---|---|
16.48.0-8.i.1.2 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
152.48.0-8.i.1.1 | $152$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
304.48.0-304.g.1.6 | $304$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
304.48.0-304.g.1.27 | $304$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
304.48.1-304.b.1.6 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.48.1-304.b.1.27 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
304.192.1-304.g.1.3 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.192.1-304.g.2.3 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.192.1-304.i.1.6 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.192.1-304.i.2.9 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.192.1-304.p.1.1 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.192.1-304.p.2.6 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.192.1-304.r.1.1 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.192.1-304.r.2.7 | $304$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
304.192.3-304.bl.1.8 | $304$ | $2$ | $2$ | $3$ | $?$ | not computed |
304.192.3-304.bu.1.6 | $304$ | $2$ | $2$ | $3$ | $?$ | not computed |
304.192.3-304.bu.2.11 | $304$ | $2$ | $2$ | $3$ | $?$ | not computed |
304.192.3-304.bx.1.6 | $304$ | $2$ | $2$ | $3$ | $?$ | not computed |
304.192.3-304.cb.1.8 | $304$ | $2$ | $2$ | $3$ | $?$ | not computed |
304.192.3-304.ck.1.3 | $304$ | $2$ | $2$ | $3$ | $?$ | not computed |
304.192.3-304.ck.2.5 | $304$ | $2$ | $2$ | $3$ | $?$ | not computed |
304.192.3-304.cp.1.4 | $304$ | $2$ | $2$ | $3$ | $?$ | not computed |