Invariants
Level: | $70$ | $\SL_2$-level: | $10$ | Newform level: | $20$ | ||
Index: | $72$ | $\PSL_2$-index: | $72$ | ||||
Genus: | $1 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $2^{6}\cdot10^{6}$ | Cusp orbits | $3^{2}\cdot6$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | $0$ | ||||||
$\Q$-gonality: | $2 \le \gamma \le 6$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 10K1 |
Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 70.72.1.2 |
Level structure
Jacobian
Conductor: | $2^{2}\cdot5$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | 20.2.a.a |
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
Cover information
Click on a modular curve in the diagram to see information about it.
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The following modular covers realize this modular curve as a fiber product over $X(1)$.
Factor curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
5.12.0.a.2 | $5$ | $6$ | $6$ | $0$ | $0$ | full Jacobian |
14.6.0.a.1 | $14$ | $12$ | $12$ | $0$ | $0$ | full Jacobian |
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
10.24.1.a.2 | $10$ | $3$ | $3$ | $1$ | $0$ | dimension zero |
70.36.1.a.1 | $70$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
70.360.13.d.1 | $70$ | $5$ | $5$ | $13$ | $0$ | $1^{2}\cdot2^{3}\cdot4$ |
70.576.37.c.1 | $70$ | $8$ | $8$ | $37$ | $0$ | $1^{4}\cdot2^{8}\cdot4^{2}\cdot8$ |
70.1512.109.i.2 | $70$ | $21$ | $21$ | $109$ | $4$ | $1^{4}\cdot2^{12}\cdot4^{16}\cdot8^{2}$ |
70.2016.145.i.1 | $70$ | $28$ | $28$ | $145$ | $4$ | $1^{8}\cdot2^{20}\cdot4^{18}\cdot8^{3}$ |
140.144.7.bj.2 | $140$ | $2$ | $2$ | $7$ | $?$ | not computed |
140.144.7.bk.2 | $140$ | $2$ | $2$ | $7$ | $?$ | not computed |
140.144.7.bl.1 | $140$ | $2$ | $2$ | $7$ | $?$ | not computed |
140.144.7.bm.1 | $140$ | $2$ | $2$ | $7$ | $?$ | not computed |
140.144.7.bn.2 | $140$ | $2$ | $2$ | $7$ | $?$ | not computed |
140.144.7.bo.2 | $140$ | $2$ | $2$ | $7$ | $?$ | not computed |
140.144.7.bp.1 | $140$ | $2$ | $2$ | $7$ | $?$ | not computed |
140.144.7.bq.1 | $140$ | $2$ | $2$ | $7$ | $?$ | not computed |
140.288.13.fy.1 | $140$ | $4$ | $4$ | $13$ | $?$ | not computed |
210.216.13.i.1 | $210$ | $3$ | $3$ | $13$ | $?$ | not computed |
210.288.13.c.2 | $210$ | $4$ | $4$ | $13$ | $?$ | not computed |
280.144.7.or.2 | $280$ | $2$ | $2$ | $7$ | $?$ | not computed |
280.144.7.os.1 | $280$ | $2$ | $2$ | $7$ | $?$ | not computed |
280.144.7.ot.1 | $280$ | $2$ | $2$ | $7$ | $?$ | not computed |
280.144.7.ou.2 | $280$ | $2$ | $2$ | $7$ | $?$ | not computed |
280.144.7.ov.2 | $280$ | $2$ | $2$ | $7$ | $?$ | not computed |
280.144.7.ow.1 | $280$ | $2$ | $2$ | $7$ | $?$ | not computed |
280.144.7.ox.1 | $280$ | $2$ | $2$ | $7$ | $?$ | not computed |
280.144.7.oy.2 | $280$ | $2$ | $2$ | $7$ | $?$ | not computed |