LMFDB - Modular curve $X

Invariants

Level:	$104$	$\SL_2$-level:	$104$	Newform level:	$1$
Index:	$168$	$\PSL_2$-index:	$168$
Genus:	$11 = 1 + \frac{ 168 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$
Cusps:	$8$ (all of which are rational)	Cusp widths	$1^{2}\cdot2\cdot8\cdot13^{2}\cdot26\cdot104$	Cusp orbits	$1^{8}$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
Analytic rank:	not computed
$\Q$-gonality:	$4 \le \gamma \le 11$
$\overline{\Q}$-gonality:	$4 \le \gamma \le 11$
Rational cusps:	$8$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:

104D11

Level structure

$\GL_2(\Z/104\Z)$-generators:	$\begin{bmatrix}23&37\\0&85\end{bmatrix}$, $\begin{bmatrix}29&55\\0&51\end{bmatrix}$, $\begin{bmatrix}57&27\\0&31\end{bmatrix}$, $\begin{bmatrix}61&36\\0&49\end{bmatrix}$, $\begin{bmatrix}75&82\\0&85\end{bmatrix}$, $\begin{bmatrix}95&81\\0&41\end{bmatrix}$, $\begin{bmatrix}101&62\\0&15\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	104.336.11-104.bx.1.1, 104.336.11-104.bx.1.2, 104.336.11-104.bx.1.3, 104.336.11-104.bx.1.4, 104.336.11-104.bx.1.5, 104.336.11-104.bx.1.6, 104.336.11-104.bx.1.7, 104.336.11-104.bx.1.8, 104.336.11-104.bx.1.9, 104.336.11-104.bx.1.10, 104.336.11-104.bx.1.11, 104.336.11-104.bx.1.12, 104.336.11-104.bx.1.13, 104.336.11-104.bx.1.14, 104.336.11-104.bx.1.15, 104.336.11-104.bx.1.16, 104.336.11-104.bx.1.17, 104.336.11-104.bx.1.18, 104.336.11-104.bx.1.19, 104.336.11-104.bx.1.20, 104.336.11-104.bx.1.21, 104.336.11-104.bx.1.22, 104.336.11-104.bx.1.23, 104.336.11-104.bx.1.24, 104.336.11-104.bx.1.25, 104.336.11-104.bx.1.26, 104.336.11-104.bx.1.27, 104.336.11-104.bx.1.28, 104.336.11-104.bx.1.29, 104.336.11-104.bx.1.30, 104.336.11-104.bx.1.31, 104.336.11-104.bx.1.32, 104.336.11-104.bx.1.33, 104.336.11-104.bx.1.34, 104.336.11-104.bx.1.35, 104.336.11-104.bx.1.36, 104.336.11-104.bx.1.37, 104.336.11-104.bx.1.38, 104.336.11-104.bx.1.39, 104.336.11-104.bx.1.40, 104.336.11-104.bx.1.41, 104.336.11-104.bx.1.42, 104.336.11-104.bx.1.43, 104.336.11-104.bx.1.44, 104.336.11-104.bx.1.45, 104.336.11-104.bx.1.46, 104.336.11-104.bx.1.47, 104.336.11-104.bx.1.48, 208.336.11-104.bx.1.1, 208.336.11-104.bx.1.2, 208.336.11-104.bx.1.3, 208.336.11-104.bx.1.4, 208.336.11-104.bx.1.5, 208.336.11-104.bx.1.6, 208.336.11-104.bx.1.7, 208.336.11-104.bx.1.8, 208.336.11-104.bx.1.9, 208.336.11-104.bx.1.10, 208.336.11-104.bx.1.11, 208.336.11-104.bx.1.12, 208.336.11-104.bx.1.13, 208.336.11-104.bx.1.14, 208.336.11-104.bx.1.15, 208.336.11-104.bx.1.16, 208.336.11-104.bx.1.17, 208.336.11-104.bx.1.18, 208.336.11-104.bx.1.19, 208.336.11-104.bx.1.20, 208.336.11-104.bx.1.21, 208.336.11-104.bx.1.22, 208.336.11-104.bx.1.23, 208.336.11-104.bx.1.24, 208.336.11-104.bx.1.25, 208.336.11-104.bx.1.26, 208.336.11-104.bx.1.27, 208.336.11-104.bx.1.28, 208.336.11-104.bx.1.29, 208.336.11-104.bx.1.30, 208.336.11-104.bx.1.31, 208.336.11-104.bx.1.32, 312.336.11-104.bx.1.1, 312.336.11-104.bx.1.2, 312.336.11-104.bx.1.3, 312.336.11-104.bx.1.4, 312.336.11-104.bx.1.5, 312.336.11-104.bx.1.6, 312.336.11-104.bx.1.7, 312.336.11-104.bx.1.8, 312.336.11-104.bx.1.9, 312.336.11-104.bx.1.10, 312.336.11-104.bx.1.11, 312.336.11-104.bx.1.12, 312.336.11-104.bx.1.13, 312.336.11-104.bx.1.14, 312.336.11-104.bx.1.15, 312.336.11-104.bx.1.16, 312.336.11-104.bx.1.17, 312.336.11-104.bx.1.18, 312.336.11-104.bx.1.19, 312.336.11-104.bx.1.20, 312.336.11-104.bx.1.21, 312.336.11-104.bx.1.22, 312.336.11-104.bx.1.23, 312.336.11-104.bx.1.24, 312.336.11-104.bx.1.25, 312.336.11-104.bx.1.26, 312.336.11-104.bx.1.27, 312.336.11-104.bx.1.28, 312.336.11-104.bx.1.29, 312.336.11-104.bx.1.30, 312.336.11-104.bx.1.31, 312.336.11-104.bx.1.32, 312.336.11-104.bx.1.33, 312.336.11-104.bx.1.34, 312.336.11-104.bx.1.35, 312.336.11-104.bx.1.36, 312.336.11-104.bx.1.37, 312.336.11-104.bx.1.38, 312.336.11-104.bx.1.39, 312.336.11-104.bx.1.40, 312.336.11-104.bx.1.41, 312.336.11-104.bx.1.42, 312.336.11-104.bx.1.43, 312.336.11-104.bx.1.44, 312.336.11-104.bx.1.45, 312.336.11-104.bx.1.46, 312.336.11-104.bx.1.47, 312.336.11-104.bx.1.48
Cyclic 104-isogeny field degree:	$1$
Cyclic 104-torsion field degree:	$48$
Full 104-torsion field degree:	$239616$

Rational points

This modular curve has 8 rational cusps but no known non-cuspidal rational points.

Modular covers

The following modular covers realize this modular curve as a fiber product over $X(1)$.

Factor curve	Level	Index	Degree	Genus	Rank
$X_0(8)$	$8$	$14$	$14$	$0$	$0$
$X_0(13)$	$13$	$12$	$12$	$0$	$0$

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank
$X_0(8)$	$8$	$14$	$14$	$0$	$0$
$X_0(52)$	$52$	$2$	$2$	$5$	$0$

This modular curve is minimally covered by the modular curves in the database listed below.

Covering curve	Level	Index	Degree	Genus
104.336.21.gn.1	$104$	$2$	$2$	$21$
104.336.21.gn.2	$104$	$2$	$2$	$21$
104.336.21.gp.1	$104$	$2$	$2$	$21$
104.336.21.gp.2	$104$	$2$	$2$	$21$
104.336.21.gr.1	$104$	$2$	$2$	$21$
104.336.21.gr.2	$104$	$2$	$2$	$21$
104.336.21.gt.1	$104$	$2$	$2$	$21$
104.336.21.gt.2	$104$	$2$	$2$	$21$
104.336.23.br.1	$104$	$2$	$2$	$23$
104.336.23.bx.1	$104$	$2$	$2$	$23$
104.336.23.cl.1	$104$	$2$	$2$	$23$
104.336.23.cm.1	$104$	$2$	$2$	$23$
104.336.23.ec.1	$104$	$2$	$2$	$23$
104.336.23.ee.1	$104$	$2$	$2$	$23$
104.336.23.eg.1	$104$	$2$	$2$	$23$
104.336.23.ei.1	$104$	$2$	$2$	$23$
104.336.23.fn.1	$104$	$2$	$2$	$23$
104.336.23.fn.2	$104$	$2$	$2$	$23$
104.336.23.fo.1	$104$	$2$	$2$	$23$
104.336.23.fo.2	$104$	$2$	$2$	$23$
104.336.23.fp.1	$104$	$2$	$2$	$23$
104.336.23.fp.2	$104$	$2$	$2$	$23$
104.336.23.fp.3	$104$	$2$	$2$	$23$
104.336.23.fp.4	$104$	$2$	$2$	$23$
104.336.23.fq.1	$104$	$2$	$2$	$23$
104.336.23.fq.2	$104$	$2$	$2$	$23$
104.336.23.fq.3	$104$	$2$	$2$	$23$
104.336.23.fq.4	$104$	$2$	$2$	$23$
104.336.23.fr.1	$104$	$2$	$2$	$23$
104.336.23.fr.2	$104$	$2$	$2$	$23$
104.336.23.fs.1	$104$	$2$	$2$	$23$
104.336.23.fs.2	$104$	$2$	$2$	$23$
104.336.23.fu.1	$104$	$2$	$2$	$23$
104.336.23.fu.2	$104$	$2$	$2$	$23$
104.336.23.fw.1	$104$	$2$	$2$	$23$
104.336.23.fw.2	$104$	$2$	$2$	$23$
104.336.23.fy.1	$104$	$2$	$2$	$23$
104.336.23.fy.2	$104$	$2$	$2$	$23$
104.336.23.ga.1	$104$	$2$	$2$	$23$
104.336.23.ga.2	$104$	$2$	$2$	$23$
208.336.23.bg.1	$208$	$2$	$2$	$23$
208.336.23.bg.2	$208$	$2$	$2$	$23$
208.336.23.bh.1	$208$	$2$	$2$	$23$
208.336.23.bh.2	$208$	$2$	$2$	$23$
208.336.23.bs.1	$208$	$2$	$2$	$23$
208.336.23.bs.2	$208$	$2$	$2$	$23$
208.336.23.bt.1	$208$	$2$	$2$	$23$
208.336.23.bt.2	$208$	$2$	$2$	$23$
208.336.23.bu.1	$208$	$2$	$2$	$23$
208.336.23.bu.2	$208$	$2$	$2$	$23$
208.336.23.bu.3	$208$	$2$	$2$	$23$
208.336.23.bu.4	$208$	$2$	$2$	$23$
208.336.23.bv.1	$208$	$2$	$2$	$23$
208.336.23.bv.2	$208$	$2$	$2$	$23$
208.336.23.bv.3	$208$	$2$	$2$	$23$
208.336.23.bv.4	$208$	$2$	$2$	$23$
208.336.23.bw.1	$208$	$2$	$2$	$23$
208.336.23.bw.2	$208$	$2$	$2$	$23$
208.336.23.bx.1	$208$	$2$	$2$	$23$
208.336.23.bx.2	$208$	$2$	$2$	$23$
208.336.23.by.1	$208$	$2$	$2$	$23$
208.336.23.bz.1	$208$	$2$	$2$	$23$
$X_0(208)$	$208$	$2$	$2$	$23$
208.336.23.cd.1	$208$	$2$	$2$	$23$
312.336.21.yz.1	$312$	$2$	$2$	$21$
312.336.21.yz.2	$312$	$2$	$2$	$21$
312.336.21.zb.1	$312$	$2$	$2$	$21$
312.336.21.zb.2	$312$	$2$	$2$	$21$
312.336.21.zd.1	$312$	$2$	$2$	$21$
312.336.21.zd.2	$312$	$2$	$2$	$21$
312.336.21.zf.1	$312$	$2$	$2$	$21$
312.336.21.zf.2	$312$	$2$	$2$	$21$
312.336.23.fs.1	$312$	$2$	$2$	$23$
312.336.23.fu.1	$312$	$2$	$2$	$23$
312.336.23.fw.1	$312$	$2$	$2$	$23$
312.336.23.fy.1	$312$	$2$	$2$	$23$
312.336.23.iu.1	$312$	$2$	$2$	$23$
312.336.23.iw.1	$312$	$2$	$2$	$23$
312.336.23.iy.1	$312$	$2$	$2$	$23$
312.336.23.ja.1	$312$	$2$	$2$	$23$
312.336.23.kx.1	$312$	$2$	$2$	$23$
312.336.23.kx.2	$312$	$2$	$2$	$23$
312.336.23.ky.1	$312$	$2$	$2$	$23$
312.336.23.ky.2	$312$	$2$	$2$	$23$
312.336.23.kz.1	$312$	$2$	$2$	$23$
312.336.23.kz.2	$312$	$2$	$2$	$23$
312.336.23.kz.3	$312$	$2$	$2$	$23$
312.336.23.kz.4	$312$	$2$	$2$	$23$
312.336.23.la.1	$312$	$2$	$2$	$23$
312.336.23.la.2	$312$	$2$	$2$	$23$
312.336.23.la.3	$312$	$2$	$2$	$23$
312.336.23.la.4	$312$	$2$	$2$	$23$
312.336.23.lb.1	$312$	$2$	$2$	$23$
312.336.23.lb.2	$312$	$2$	$2$	$23$
312.336.23.lc.1	$312$	$2$	$2$	$23$
312.336.23.lc.2	$312$	$2$	$2$	$23$
312.336.23.le.1	$312$	$2$	$2$	$23$
312.336.23.le.2	$312$	$2$	$2$	$23$
312.336.23.lg.1	$312$	$2$	$2$	$23$
312.336.23.lg.2	$312$	$2$	$2$	$23$
312.336.23.li.1	$312$	$2$	$2$	$23$
312.336.23.li.2	$312$	$2$	$2$	$23$
312.336.23.lk.1	$312$	$2$	$2$	$23$
312.336.23.lk.2	$312$	$2$	$2$	$23$

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Invariants

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Level structure

Rational points

Modular covers

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	104.168.11.bx.1
Level	$104$
Index	$168$
Genus	$11$

Cusps	$8$
$\Q$-cusps	$8$