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: | $\begin{bmatrix}1&36\\76&73\end{bmatrix}$, $\begin{bmatrix}25&40\\72&67\end{bmatrix}$, $\begin{bmatrix}33&80\\100&43\end{bmatrix}$, $\begin{bmatrix}65&80\\44&71\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 104.96.1.x.1 for the level structure with $-I$) |
Cyclic 104-isogeny field degree: | $28$ |
Cyclic 104-torsion field degree: | $336$ |
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.1.1 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
104.96.0-104.b.2.9 | $104$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
104.96.0-104.b.2.23 | $104$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
104.96.0-8.c.1.2 | $104$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
104.96.0-104.w.1.2 | $104$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
104.96.0-104.w.1.15 | $104$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
104.96.0-104.x.1.2 | $104$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
104.96.0-104.x.1.13 | $104$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
104.96.1-104.o.2.1 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.o.2.2 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.be.2.8 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.be.2.9 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.bf.2.10 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.bf.2.13 | $104$ | $2$ | $2$ | $1$ | $?$ | 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.x.1.1 | $104$ | $2$ | $2$ | $5$ | $?$ | not computed |
104.384.5-104.y.2.2 | $104$ | $2$ | $2$ | $5$ | $?$ | not computed |
104.384.5-104.ba.2.2 | $104$ | $2$ | $2$ | $5$ | $?$ | not computed |
104.384.5-104.bb.3.1 | $104$ | $2$ | $2$ | $5$ | $?$ | not computed |
208.384.5-208.f.1.1 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |
208.384.5-208.l.2.2 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |
208.384.5-208.bh.1.4 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |
208.384.5-208.bj.1.2 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |
208.384.5-208.eo.1.2 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |
208.384.5-208.eq.1.1 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |
208.384.5-208.fm.2.3 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |
208.384.5-208.fs.1.1 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.hi.2.1 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.hk.2.3 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.hs.2.2 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.hu.1.1 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |