Invariants
| Level: | $120$ | $\SL_2$-level: | $8$ | Newform level: | $576$ | ||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (of which $2$ are rational) | Cusp widths | $4^{4}\cdot8^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}$ | ||
| 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: | 8G1 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}21&62\\80&77\end{bmatrix}$, $\begin{bmatrix}45&76\\104&91\end{bmatrix}$, $\begin{bmatrix}47&46\\76&79\end{bmatrix}$, $\begin{bmatrix}55&62\\48&113\end{bmatrix}$, $\begin{bmatrix}113&116\\72&43\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 24.48.1.bi.2 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $48$ |
| Cyclic 120-torsion field degree: | $1536$ |
| Full 120-torsion field degree: | $368640$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | 576.2.a.c |
Models
Weierstrass model Weierstrass model
| $ y^{2} $ | $=$ | $ x^{3} - 396x + 3024 $ |
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 48 from the Weierstrass model of this modular curve to the modular curve $X(1)$ :
| $\displaystyle j$ | $=$ | $\displaystyle -\frac{1}{2^2\cdot3^2}\cdot\frac{144x^{2}y^{14}-550522656x^{2}y^{12}z^{2}+283165527573504x^{2}y^{10}z^{4}-35589093251396649984x^{2}y^{8}z^{6}+1435852678252338286166016x^{2}y^{6}z^{8}-23600740106397378551611981824x^{2}y^{4}z^{10}+166825072115401190726981684035584x^{2}y^{2}z^{12}-421596930836809960564255254978232320x^{2}z^{14}-37296xy^{14}z+51202720512xy^{12}z^{3}-17060703549398784xy^{10}z^{5}+1487230108714945769472xy^{8}z^{7}-47478377603511577592856576xy^{6}z^{9}+665298645524533817351278166016xy^{4}z^{11}-4187262207135015339241996903514112xy^{2}z^{13}+9684318754352320554987748010250731520xz^{15}-y^{16}+4344192y^{14}z^{2}-4058589950208y^{12}z^{4}+792268224762138624y^{10}z^{6}-43843111579283454738432y^{8}z^{8}+944128051414930556653142016y^{6}z^{10}-9065075431123430510805612232704y^{4}z^{12}+38280102371311259261797843561611264y^{2}z^{14}-55501867011727212343338600744464941056z^{16}}{zy^{4}(10332x^{2}y^{8}z-519436800x^{2}y^{6}z^{3}+3852738452736x^{2}y^{4}z^{5}-1451188224x^{2}y^{2}z^{7}+78364164096x^{2}z^{9}+xy^{10}-516240xy^{8}z^{2}+15177570048xy^{6}z^{4}-88499423895552xy^{4}z^{6}-15237476352xy^{2}z^{8}+940369969152xz^{10}-144y^{10}z+16907616y^{8}z^{3}-217503553536y^{6}z^{5}+507198870484992y^{4}z^{7}+417942208512y^{2}z^{9}-19747769352192z^{11})}$ |
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 40.48.0-8.e.1.5 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 120.48.0-8.e.1.9 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.48.0-24.h.2.6 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.48.0-24.h.2.21 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.48.1-24.d.1.11 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.48.1-24.d.1.12 | $120$ | $2$ | $2$ | $1$ | $?$ | 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 |
|---|---|---|---|---|---|---|
| 120.192.1-24.g.2.6 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-24.w.1.5 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-24.bl.1.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-24.bp.2.2 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-24.bu.1.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-24.by.2.6 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-24.cf.2.4 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-24.ch.1.2 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.288.9-24.hd.2.11 | $120$ | $3$ | $3$ | $9$ | $?$ | not computed |
| 120.384.9-24.eh.2.4 | $120$ | $4$ | $4$ | $9$ | $?$ | not computed |
| 120.192.1-120.hc.1.14 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.hg.1.9 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.hs.1.13 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.hw.1.12 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.jo.1.9 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.js.1.12 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.ke.1.16 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.ki.1.9 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.480.17-120.dp.2.18 | $120$ | $5$ | $5$ | $17$ | $?$ | not computed |