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: | $\begin{bmatrix}13&14\\42&89\end{bmatrix}$, $\begin{bmatrix}59&10\\36&79\end{bmatrix}$, $\begin{bmatrix}59&30\\18&59\end{bmatrix}$, $\begin{bmatrix}63&2\\86&81\end{bmatrix}$, $\begin{bmatrix}71&90\\54&77\end{bmatrix}$, $\begin{bmatrix}103&110\\66&11\end{bmatrix}$ |
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.1.2 | $120$ | $4$ | $4$ | $0$ | $?$ | 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.1.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-24.cp.1.8 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-24.cp.2.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-24.cp.2.8 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-24.cp.3.4 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-24.cp.3.5 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-24.cp.4.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-24.cp.4.6 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ll.1.2 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ll.1.12 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ll.2.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ll.2.13 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ll.3.2 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ll.3.8 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ll.4.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ll.4.13 | $120$ | $2$ | $2$ | $1$ | $?$ | 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.1.1 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-24.be.1.10 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-24.bf.1.10 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-24.bf.1.17 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-24.bg.1.3 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-24.bg.1.13 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-24.cc.1.3 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-24.cc.1.13 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-24.cc.2.5 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-24.cc.2.10 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-24.cd.1.2 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-24.cd.1.13 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-24.cd.2.3 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-24.cd.2.10 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.ej.1.6 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.ej.1.13 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.ek.1.19 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.ek.1.29 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.em.1.27 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.em.1.29 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.en.1.5 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.en.1.6 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.fi.1.18 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.fi.1.19 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.fi.2.18 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.fi.2.19 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.fj.1.17 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.fj.1.20 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.fj.2.17 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.fj.2.20 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.288.5-24.m.1.4 | $120$ | $3$ | $3$ | $5$ | $?$ | not computed |
120.480.17-120.fj.1.9 | $120$ | $5$ | $5$ | $17$ | $?$ | not computed |