Invariants
| Level: | $120$ | $\SL_2$-level: | $10$ | Newform level: | $1600$ | ||
| Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (of which $2$ are rational) | Cusp widths | $2^{2}\cdot10^{2}$ | Cusp orbits | $1^{2}\cdot2$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 10D1 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}16&9\\93&80\end{bmatrix}$, $\begin{bmatrix}34&21\\67&100\end{bmatrix}$, $\begin{bmatrix}83&55\\91&94\end{bmatrix}$, $\begin{bmatrix}111&19\\118&5\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 40.24.1.cj.2 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $48$ |
| Cyclic 120-torsion field degree: | $1536$ |
| Full 120-torsion field degree: | $737280$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | 1600.2.a.w |
Models
Weierstrass model Weierstrass model
| $ y^{2} $ | $=$ | $ x^{3} - x^{2} - 4133x + 103637 $ |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Maps to other modular curves
$j$-invariant map of degree 24 from the Weierstrass model of this modular curve to the modular curve $X(1)$ :
| $\displaystyle j$ | $=$ | $\displaystyle \frac{1}{2\cdot5}\cdot\frac{7280x^{2}y^{6}-6150536400000x^{2}y^{4}z^{2}+15649414055440000000x^{2}y^{2}z^{4}-4579162597656240000000000x^{2}z^{6}-18612320xy^{6}z+1187760448800000xy^{4}z^{3}-1541479492441760000000xy^{2}z^{5}+342987060546875360000000000xz^{7}-y^{8}+18913549520y^{6}z^{2}-146611209496000000y^{4}z^{4}+76900976582267760000000y^{2}z^{6}-6421647644042996760000000000z^{8}}{y^{2}(x^{2}y^{4}-22000x^{2}y^{2}z^{2}-1000000x^{2}z^{4}+146xy^{4}z-782000xy^{2}z^{3}-36000000xz^{5}+5129y^{4}z^{2}+62352000y^{2}z^{4}+2801000000z^{6})}$ |
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 30.24.0-5.a.2.2 | $30$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 120.24.0-5.a.2.4 | $120$ | $2$ | $2$ | $0$ | $?$ | 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 |
|---|---|---|---|---|---|---|
| 120.144.1-40.ba.2.8 | $120$ | $3$ | $3$ | $1$ | $?$ | dimension zero |
| 120.192.5-40.n.2.1 | $120$ | $4$ | $4$ | $5$ | $?$ | not computed |
| 120.240.5-40.cx.1.2 | $120$ | $5$ | $5$ | $5$ | $?$ | not computed |
| 120.144.5-120.baz.1.11 | $120$ | $3$ | $3$ | $5$ | $?$ | not computed |
| 120.192.5-120.nd.1.31 | $120$ | $4$ | $4$ | $5$ | $?$ | not computed |