Invariants
| Level: | $120$ | $\SL_2$-level: | $8$ | Newform level: | $800$ | ||
| 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 | $4^{2}\cdot8^{2}$ | 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: | 8B1 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}11&79\\16&25\end{bmatrix}$, $\begin{bmatrix}13&60\\116&49\end{bmatrix}$, $\begin{bmatrix}77&62\\16&17\end{bmatrix}$, $\begin{bmatrix}109&98\\116&81\end{bmatrix}$, $\begin{bmatrix}113&71\\112&15\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 40.24.1.m.1 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: | 800.2.a.d |
Models
Weierstrass model Weierstrass model
| $ y^{2} $ | $=$ | $ x^{3} + 100x $ |
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 $X(1)$ :
| $\displaystyle j$ | $=$ | $\displaystyle -\frac{2^2}{5^2}\cdot\frac{7230000x^{2}y^{4}z^{2}-40950000000000x^{2}z^{6}-4600xy^{6}z+819300000000xy^{2}z^{5}+y^{8}-4140000000y^{4}z^{4}+1000000000000z^{8}}{zy^{4}(100x^{2}z+xy^{2}+10000z^{3})}$ |
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 12.24.0-4.d.1.2 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 120.24.0-4.d.1.3 | $120$ | $2$ | $2$ | $0$ | $?$ | 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 |
|---|---|---|---|---|---|---|
| 120.96.1-40.cw.1.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-40.cx.1.6 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-40.dj.1.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-40.dk.1.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-40.dw.1.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-40.ed.1.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-40.em.1.4 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-40.ep.1.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.jh.1.6 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.jl.1.5 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.lf.1.8 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.lk.1.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.mi.1.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.mt.1.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.ob.1.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.of.1.7 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.144.5-120.bw.1.32 | $120$ | $3$ | $3$ | $5$ | $?$ | not computed |
| 120.192.5-120.bg.1.15 | $120$ | $4$ | $4$ | $5$ | $?$ | not computed |
| 120.240.9-40.ba.1.7 | $120$ | $5$ | $5$ | $9$ | $?$ | not computed |
| 120.288.9-40.bu.1.13 | $120$ | $6$ | $6$ | $9$ | $?$ | not computed |
| 120.480.17-40.he.1.10 | $120$ | $10$ | $10$ | $17$ | $?$ | not computed |