Invariants
Level: | $104$ | $\SL_2$-level: | $8$ | ||||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot8^{4}$ | Cusp orbits | $2^{5}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $1 \le \gamma \le 2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8O0 |
Level structure
$\GL_2(\Z/104\Z)$-generators: | $\begin{bmatrix}23&48\\88&43\end{bmatrix}$, $\begin{bmatrix}41&40\\10&45\end{bmatrix}$, $\begin{bmatrix}63&84\\10&65\end{bmatrix}$, $\begin{bmatrix}97&100\\94&33\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 104.48.0.t.1 for the level structure with $-I$) |
Cyclic 104-isogeny field degree: | $28$ |
Cyclic 104-torsion field degree: | $1344$ |
Full 104-torsion field degree: | $419328$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
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 |
---|---|---|---|---|---|
8.48.0-8.e.1.5 | $8$ | $2$ | $2$ | $0$ | $0$ |
104.48.0-8.e.1.16 | $104$ | $2$ | $2$ | $0$ | $?$ |
104.48.0-104.i.1.23 | $104$ | $2$ | $2$ | $0$ | $?$ |
104.48.0-104.i.1.28 | $104$ | $2$ | $2$ | $0$ | $?$ |
104.48.0-104.l.1.3 | $104$ | $2$ | $2$ | $0$ | $?$ |
104.48.0-104.l.1.17 | $104$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
104.192.1-104.r.1.7 | $104$ | $2$ | $2$ | $1$ |
104.192.1-104.u.1.1 | $104$ | $2$ | $2$ | $1$ |
104.192.1-104.w.1.3 | $104$ | $2$ | $2$ | $1$ |
104.192.1-104.z.1.3 | $104$ | $2$ | $2$ | $1$ |
104.192.1-104.be.1.5 | $104$ | $2$ | $2$ | $1$ |
104.192.1-104.bf.1.1 | $104$ | $2$ | $2$ | $1$ |
104.192.1-104.bg.1.1 | $104$ | $2$ | $2$ | $1$ |
104.192.1-104.bh.1.5 | $104$ | $2$ | $2$ | $1$ |
312.192.1-312.im.1.14 | $312$ | $2$ | $2$ | $1$ |
312.192.1-312.in.1.15 | $312$ | $2$ | $2$ | $1$ |
312.192.1-312.iq.2.8 | $312$ | $2$ | $2$ | $1$ |
312.192.1-312.ir.2.8 | $312$ | $2$ | $2$ | $1$ |
312.192.1-312.js.2.4 | $312$ | $2$ | $2$ | $1$ |
312.192.1-312.jt.2.16 | $312$ | $2$ | $2$ | $1$ |
312.192.1-312.jw.1.16 | $312$ | $2$ | $2$ | $1$ |
312.192.1-312.jx.1.11 | $312$ | $2$ | $2$ | $1$ |
312.288.8-312.np.2.64 | $312$ | $3$ | $3$ | $8$ |
312.384.7-312.ht.2.57 | $312$ | $4$ | $4$ | $7$ |