Invariants
Level: | $104$ | $\SL_2$-level: | $8$ | 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 | $4^{2}\cdot8^{2}$ | 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: | 8B1 |
Level structure
$\GL_2(\Z/104\Z)$-generators: | $\begin{bmatrix}25&20\\80&93\end{bmatrix}$, $\begin{bmatrix}45&20\\20&59\end{bmatrix}$, $\begin{bmatrix}51&72\\48&31\end{bmatrix}$, $\begin{bmatrix}63&20\\0&21\end{bmatrix}$, $\begin{bmatrix}101&86\\64&91\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 104.24.1.c.1 for the level structure with $-I$) |
Cyclic 104-isogeny field degree: | $28$ |
Cyclic 104-torsion field degree: | $1344$ |
Full 104-torsion field degree: | $838656$ |
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 |
---|---|---|---|---|---|---|
8.24.0-4.b.1.10 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
104.24.0-4.b.1.3 | $104$ | $2$ | $2$ | $0$ | $?$ | 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 |
---|---|---|---|---|---|---|
104.96.1-104.o.2.3 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.o.2.11 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.v.1.9 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.v.1.13 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.bc.1.3 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.bc.1.7 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.bc.2.7 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.bc.2.8 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.bd.1.6 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.bd.1.14 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.bd.2.4 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.bd.2.12 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.be.1.11 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.be.1.15 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.be.2.10 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.be.2.14 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.bf.1.4 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.bf.1.8 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.bf.2.5 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.bf.2.6 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.bt.1.9 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.bt.1.11 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.bu.1.5 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.96.1-104.bu.1.7 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.bs.1.14 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.bs.1.22 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.bx.1.22 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.bx.1.32 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.dk.1.8 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.dk.1.32 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.dk.2.13 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.dk.2.31 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.dl.1.17 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.dl.1.29 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.dl.2.6 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.dl.2.24 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.dm.1.18 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.dm.1.28 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.dm.2.3 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.dm.2.27 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.dn.1.13 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.dn.1.31 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.dn.2.26 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.dn.2.32 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.ez.1.20 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.ez.1.32 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.fd.1.12 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.fd.1.20 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.144.5-312.c.1.28 | $312$ | $3$ | $3$ | $5$ | $?$ | not computed |
312.192.5-312.c.1.69 | $312$ | $4$ | $4$ | $5$ | $?$ | not computed |