Invariants
| Level: | $120$ | $\SL_2$-level: | $12$ | 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 $4$ are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot6^{2}\cdot12^{2}$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 12P1 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}7&80\\60&83\end{bmatrix}$, $\begin{bmatrix}9&88\\52&21\end{bmatrix}$, $\begin{bmatrix}59&58\\90&7\end{bmatrix}$, $\begin{bmatrix}75&58\\34&15\end{bmatrix}$, $\begin{bmatrix}97&74\\28&9\end{bmatrix}$, $\begin{bmatrix}105&76\\94&75\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 24.48.1.bz.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $24$ |
| Cyclic 120-torsion field degree: | $768$ |
| Full 120-torsion field degree: | $368640$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | 576.2.a.b |
Models
Weierstrass model Weierstrass model
| $ y^{2} $ | $=$ | $ x^{3} - 156x + 560 $ |
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 $X(1)$ :
| $\displaystyle j$ | $=$ | $\displaystyle \frac{1}{2^6\cdot3^6}\cdot\frac{96x^{2}y^{14}-3071520x^{2}y^{12}z^{2}+19167777792x^{2}y^{10}z^{4}-73205492290560x^{2}y^{8}z^{6}+168881565187768320x^{2}y^{6}z^{8}-266227264601441501184x^{2}y^{4}z^{10}+247916413700751470100480x^{2}y^{2}z^{12}-134702959110560452221861888x^{2}z^{14}-4368xy^{14}z+69361920xy^{12}z^{3}-383703236352xy^{10}z^{5}+1313691284017152xy^{8}z^{7}-2857875029712175104xy^{6}z^{9}+4206511845249122304000xy^{4}z^{11}-3838872231829646418640896xy^{2}z^{13}+1872592528727280463160279040xz^{15}-y^{16}+124800y^{14}z^{2}-1014923520y^{12}z^{4}+4497071063040y^{10}z^{6}-11992345692291072y^{8}z^{8}+22043062823581384704y^{6}z^{10}-25772226110498737225728y^{4}z^{12}+18749649047391718128746496y^{2}z^{14}-5335126223420150253550043136z^{16}}{z^{4}y^{4}(72x^{2}y^{6}-1191024x^{2}y^{4}z^{2}+3630210048x^{2}y^{2}z^{4}-2971852084224x^{2}z^{6}-2520xy^{6}z+23556096xy^{4}z^{3}-57717764352xy^{2}z^{5}+41609194352640xz^{7}-y^{8}+56448y^{6}z^{2}-255633408y^{4}z^{4}+337961134080y^{2}z^{6}-118906735104000z^{8})}$ |
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 60.48.0-6.a.1.6 | $60$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 120.24.0-24.b.1.3 | $120$ | $4$ | $4$ | $0$ | $?$ | full Jacobian |
| 120.48.0-6.a.1.7 | $120$ | $2$ | $2$ | $0$ | $?$ | 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 |
|---|---|---|---|---|---|---|
| 120.192.1-24.cp.1.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-24.cp.1.6 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-24.cp.2.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-24.cp.2.6 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-24.cp.3.2 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-24.cp.3.7 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-24.cp.4.2 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-24.cp.4.7 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.ll.1.5 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.ll.1.15 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.ll.2.4 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.ll.2.16 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.ll.3.9 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.ll.3.15 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.ll.4.4 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.ll.4.16 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.3-24.bd.1.3 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-24.bd.1.7 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-24.be.1.5 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-24.be.1.14 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-24.bf.1.14 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-24.bf.1.19 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-24.bg.1.1 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-24.bg.1.15 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-24.cc.1.7 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-24.cc.1.9 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-24.cc.2.2 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-24.cc.2.13 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-24.cd.1.6 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-24.cd.1.9 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-24.cd.2.2 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-24.cd.2.11 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.ej.1.17 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.ej.1.26 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.ek.1.2 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.ek.1.16 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.em.1.2 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.em.1.8 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.en.1.25 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.en.1.26 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.fi.1.6 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.fi.1.7 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.fi.2.6 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.fi.2.7 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.fj.1.5 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.fj.1.8 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.fj.2.5 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.fj.2.8 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.288.5-24.m.1.8 | $120$ | $3$ | $3$ | $5$ | $?$ | not computed |
| 120.480.17-120.fj.1.15 | $120$ | $5$ | $5$ | $17$ | $?$ | not computed |