Invariants
Level: | $104$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{8}$ | Cusp orbits | $2^{4}\cdot4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8K1 |
Level structure
$\GL_2(\Z/104\Z)$-generators: | $\begin{bmatrix}1&40\\30&61\end{bmatrix}$, $\begin{bmatrix}15&56\\36&51\end{bmatrix}$, $\begin{bmatrix}17&4\\70&43\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 104.96.1.cb.1 for the level structure with $-I$) |
Cyclic 104-isogeny field degree: | $14$ |
Cyclic 104-torsion field degree: | $672$ |
Full 104-torsion field degree: | $209664$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
8.96.0-8.k.1.6 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
104.96.0-104.i.2.3 | $104$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
104.96.0-104.i.2.11 | $104$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
104.96.0-8.k.1.3 | $104$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
104.96.0-104.k.2.7 | $104$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
104.96.0-104.k.2.8 | $104$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
104.96.0-104.bb.1.4 | $104$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
104.96.0-104.bb.1.12 | $104$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
104.96.1-104.bc.1.5 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.bc.1.7 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.be.2.7 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.be.2.14 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.bu.1.7 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.bu.1.8 | $104$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
208.384.5-208.cb.1.3 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |
208.384.5-208.dj.2.5 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |
208.384.5-208.hh.2.6 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |
208.384.5-208.ho.1.4 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |