Invariants
| Level: | $70$ | $\SL_2$-level: | $10$ | Newform level: | $4900$ | ||
| Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
| Genus: | $1 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (of which $2$ are rational) | Cusp widths | $2^{6}\cdot10^{6}$ | Cusp orbits | $1^{2}\cdot2^{3}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $1$ | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 10K1 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 70.144.1.8 |
Level structure
| $\GL_2(\Z/70\Z)$-generators: | $\begin{bmatrix}19&60\\26&47\end{bmatrix}$, $\begin{bmatrix}49&29\\30&11\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 70.72.1.f.1 for the level structure with $-I$) |
| Cyclic 70-isogeny field degree: | $8$ |
| Cyclic 70-torsion field degree: | $96$ |
| Full 70-torsion field degree: | $40320$ |
Jacobian
| Conductor: | $2^{2}\cdot5^{2}\cdot7^{2}$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | 4900.2.a.e |
Rational points
This modular curve has infinitely many rational points, including 1 stored non-cuspidal point.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 10.72.0-10.a.2.3 | $10$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 70.48.1-70.d.1.2 | $70$ | $3$ | $3$ | $1$ | $1$ | dimension zero |
| 70.72.0-10.a.2.4 | $70$ | $2$ | $2$ | $0$ | $0$ | 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 |
|---|---|---|---|---|---|---|
| 70.720.13-70.j.1.2 | $70$ | $5$ | $5$ | $13$ | $4$ | $1^{6}\cdot2^{3}$ |
| 70.1152.37-70.v.1.1 | $70$ | $8$ | $8$ | $37$ | $6$ | $1^{12}\cdot2^{8}\cdot4^{2}$ |
| 70.3024.109-70.z.1.1 | $70$ | $21$ | $21$ | $109$ | $22$ | $1^{12}\cdot2^{28}\cdot4^{10}$ |
| 70.4032.145-70.bs.1.1 | $70$ | $28$ | $28$ | $145$ | $27$ | $1^{24}\cdot2^{36}\cdot4^{12}$ |
| 140.288.5-140.cm.1.1 | $140$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 140.288.5-140.cq.1.2 | $140$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 140.288.5-140.fi.1.1 | $140$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 140.288.5-140.fk.1.1 | $140$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 140.288.5-140.go.1.1 | $140$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 140.288.5-140.gq.1.1 | $140$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 140.288.5-140.hc.1.1 | $140$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 140.288.5-140.hg.1.1 | $140$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 210.432.13-210.ca.2.1 | $210$ | $3$ | $3$ | $13$ | $?$ | not computed |
| 280.288.5-280.rj.1.1 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 280.288.5-280.sl.1.1 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 280.288.5-280.boz.1.1 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 280.288.5-280.bpn.1.1 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 280.288.5-280.bxo.1.1 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 280.288.5-280.byc.1.1 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 280.288.5-280.cbg.1.1 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 280.288.5-280.cci.1.1 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |