Invariants
| Level: | $70$ | $\SL_2$-level: | $14$ | Newform level: | $4900$ | ||
| Index: | $126$ | $\PSL_2$-index: | $126$ | ||||
| Genus: | $7 = 1 + \frac{ 126 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 9 }{2}$ | ||||||
| Cusps: | $9$ (none of which are rational) | Cusp widths | $14^{9}$ | Cusp orbits | $3\cdot6$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $2$ | ||||||
| $\Q$-gonality: | $4$ | ||||||
| $\overline{\Q}$-gonality: | $4$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | yes $\quad(D =$ $-4$) |
Other labels
| Cummins and Pauli (CP) label: | 14A7 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 70.126.7.1 |
Level structure
| $\GL_2(\Z/70\Z)$-generators: | $\begin{bmatrix}21&29\\36&31\end{bmatrix}$, $\begin{bmatrix}51&42\\48&47\end{bmatrix}$, $\begin{bmatrix}67&23\\44&17\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 70-isogeny field degree: | $48$ |
| Cyclic 70-torsion field degree: | $1152$ |
| Full 70-torsion field degree: | $46080$ |
Jacobian
| Conductor: | $2^{10}\cdot5^{10}\cdot7^{14}$ |
| Simple: | no |
| Squarefree: | yes |
| Decomposition: | $1\cdot2^{3}$ |
| Newforms: | 98.2.a.b, 2450.2.a.bj, 4900.2.a.g, 4900.2.a.y |
Rational points
This modular curve has 1 rational CM point but no rational cusps or other known rational points.
Modular covers
Cover information
Click on a modular curve in the diagram to see information about it.
|
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| $X_{\mathrm{ns}}^+(7)$ | $7$ | $6$ | $6$ | $0$ | $0$ | full Jacobian |
| 10.6.0.a.1 | $10$ | $21$ | $21$ | $0$ | $0$ | full Jacobian |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 10.6.0.a.1 | $10$ | $21$ | $21$ | $0$ | $0$ | full Jacobian |
| 14.63.2.a.1 | $14$ | $2$ | $2$ | $2$ | $0$ | $1\cdot2^{2}$ |
| 70.42.3.a.1 | $70$ | $3$ | $3$ | $3$ | $0$ | $2^{2}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 70.252.13.e.1 | $70$ | $2$ | $2$ | $13$ | $4$ | $1^{6}$ |
| 70.252.13.f.1 | $70$ | $2$ | $2$ | $13$ | $2$ | $1^{6}$ |
| 70.252.13.g.1 | $70$ | $2$ | $2$ | $13$ | $2$ | $1^{6}$ |
| 70.252.13.h.1 | $70$ | $2$ | $2$ | $13$ | $4$ | $1^{6}$ |
| 70.630.49.d.1 | $70$ | $5$ | $5$ | $49$ | $25$ | $1^{6}\cdot3^{4}\cdot4^{6}$ |
| 70.756.55.c.1 | $70$ | $6$ | $6$ | $55$ | $19$ | $1^{12}\cdot2^{18}$ |
| 70.1260.97.bg.1 | $70$ | $10$ | $10$ | $97$ | $48$ | $1^{18}\cdot2^{18}\cdot3^{4}\cdot4^{6}$ |
| 140.252.13.q.1 | $140$ | $2$ | $2$ | $13$ | $?$ | not computed |
| 140.252.13.x.1 | $140$ | $2$ | $2$ | $13$ | $?$ | not computed |
| 140.252.13.be.1 | $140$ | $2$ | $2$ | $13$ | $?$ | not computed |
| 140.252.13.bl.1 | $140$ | $2$ | $2$ | $13$ | $?$ | not computed |
| 140.252.16.q.1 | $140$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 140.252.16.s.1 | $140$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 140.252.16.bg.1 | $140$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 140.252.16.bh.1 | $140$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 140.252.16.bo.1 | $140$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 140.252.16.bp.1 | $140$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 140.252.16.bw.1 | $140$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 140.252.16.bx.1 | $140$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 140.252.16.ce.1 | $140$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 140.252.16.cf.1 | $140$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 140.252.16.cm.1 | $140$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 140.252.16.cn.1 | $140$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 140.252.16.cu.1 | $140$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 140.252.16.cv.1 | $140$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 140.252.16.dc.1 | $140$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 140.252.16.de.1 | $140$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 210.252.13.i.1 | $210$ | $2$ | $2$ | $13$ | $?$ | not computed |
| 210.252.13.l.1 | $210$ | $2$ | $2$ | $13$ | $?$ | not computed |
| 210.252.13.o.1 | $210$ | $2$ | $2$ | $13$ | $?$ | not computed |
| 210.252.13.r.1 | $210$ | $2$ | $2$ | $13$ | $?$ | not computed |
| 280.252.13.ca.1 | $280$ | $2$ | $2$ | $13$ | $?$ | not computed |
| 280.252.13.cd.1 | $280$ | $2$ | $2$ | $13$ | $?$ | not computed |
| 280.252.13.cy.1 | $280$ | $2$ | $2$ | $13$ | $?$ | not computed |
| 280.252.13.db.1 | $280$ | $2$ | $2$ | $13$ | $?$ | not computed |
| 280.252.13.dw.1 | $280$ | $2$ | $2$ | $13$ | $?$ | not computed |
| 280.252.13.dz.1 | $280$ | $2$ | $2$ | $13$ | $?$ | not computed |
| 280.252.13.eu.1 | $280$ | $2$ | $2$ | $13$ | $?$ | not computed |
| 280.252.13.ex.1 | $280$ | $2$ | $2$ | $13$ | $?$ | not computed |
| 280.252.16.bx.1 | $280$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 280.252.16.cd.1 | $280$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 280.252.16.ei.1 | $280$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 280.252.16.el.1 | $280$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 280.252.16.fg.1 | $280$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 280.252.16.fj.1 | $280$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 280.252.16.ge.1 | $280$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 280.252.16.gh.1 | $280$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 280.252.16.hc.1 | $280$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 280.252.16.hf.1 | $280$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 280.252.16.ia.1 | $280$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 280.252.16.id.1 | $280$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 280.252.16.iy.1 | $280$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 280.252.16.jb.1 | $280$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 280.252.16.jw.1 | $280$ | $2$ | $2$ | $16$ | $?$ | not computed |
| 280.252.16.kc.1 | $280$ | $2$ | $2$ | $16$ | $?$ | not computed |