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 | $2^{6}\cdot4$ | ||
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: | $\begin{bmatrix}1&56\\44&77\end{bmatrix}$, $\begin{bmatrix}55&84\\36&99\end{bmatrix}$, $\begin{bmatrix}73&64\\100&41\end{bmatrix}$, $\begin{bmatrix}87&52\\44&25\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 104.96.1.w.1 for the level structure with $-I$) |
Cyclic 104-isogeny field degree: | $28$ |
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 real points and $\Q_p$ points for $p$ not dividing the level, but no known 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.c.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
104.96.0-104.b.1.5 | $104$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
104.96.0-104.b.1.17 | $104$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
104.96.0-8.c.1.5 | $104$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
104.96.0-104.s.1.5 | $104$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
104.96.0-104.s.1.10 | $104$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
104.96.0-104.t.1.3 | $104$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
104.96.0-104.t.1.12 | $104$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
104.96.1-104.n.2.9 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.n.2.10 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.bi.2.6 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.bi.2.7 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.bj.2.7 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.bj.2.14 | $104$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
104.384.5-104.w.1.6 | $104$ | $2$ | $2$ | $5$ | $?$ | not computed |
104.384.5-104.y.1.3 | $104$ | $2$ | $2$ | $5$ | $?$ | not computed |
104.384.5-104.z.2.7 | $104$ | $2$ | $2$ | $5$ | $?$ | not computed |
104.384.5-104.bb.1.3 | $104$ | $2$ | $2$ | $5$ | $?$ | not computed |
208.384.5-208.h.1.6 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |
208.384.5-208.j.1.5 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |
208.384.5-208.bf.1.1 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |
208.384.5-208.bl.1.1 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |
208.384.5-208.em.1.3 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |
208.384.5-208.es.1.2 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |
208.384.5-208.fo.1.7 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |
208.384.5-208.fq.1.5 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.hh.1.6 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.hj.1.7 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.hq.1.7 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.ht.1.7 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |