Invariants
| Level: | $120$ | $\SL_2$-level: | $8$ | Newform level: | $576$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
| Cusps: | $16$ (of which $4$ are rational) | Cusp widths | $4^{8}\cdot8^{8}$ | Cusp orbits | $1^{4}\cdot4^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 8K1 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}7&16\\108&55\end{bmatrix}$, $\begin{bmatrix}31&100\\12&1\end{bmatrix}$, $\begin{bmatrix}77&40\\0&1\end{bmatrix}$, $\begin{bmatrix}95&16\\116&65\end{bmatrix}$, $\begin{bmatrix}115&32\\72&23\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 24.96.1.w.2 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $48$ |
| Cyclic 120-torsion field degree: | $768$ |
| Full 120-torsion field degree: | $184320$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | 576.2.a.c |
Models
Weierstrass model Weierstrass model
| $ y^{2} $ | $=$ | $ x^{3} - 36x $ |
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 96 from the Weierstrass model of this modular curve to the modular curve $X(1)$ :
| $\displaystyle j$ | $=$ | $\displaystyle \frac{1}{2^4\cdot3^4}\cdot\frac{917568x^{2}y^{28}z^{2}-28894971525120x^{2}y^{24}z^{6}+111563587010265808896x^{2}y^{20}z^{10}+34056209653755667430768640x^{2}y^{16}z^{14}+6941563527217573128746569826304x^{2}y^{12}z^{18}+618283457811084309962615892989706240x^{2}y^{8}z^{22}+10092120727282462567339509170904357666816x^{2}y^{4}z^{26}+10463509855324846890187493327062814467031040x^{2}z^{30}-288xy^{30}z+271402430976xy^{26}z^{5}-50435802925498368xy^{22}z^{9}+586513833039053567557632xy^{18}z^{13}+173142662112161437840167665664xy^{14}z^{17}+19277559549868908961948216181391360xy^{10}z^{21}+747564470096953200762450980555351654400xy^{6}z^{25}+3197183774796089395655041850743370381524992xy^{2}z^{29}+y^{32}-193715712y^{28}z^{4}+27295170017476608y^{24}z^{8}+7766608175337970335744y^{20}z^{12}+2167224764978516195681501184y^{16}z^{16}+266118841539205456536245448474624y^{12}z^{20}+14535984842876880159201240846314766336y^{8}z^{24}+80736952985464943248731368241942723821568y^{4}z^{28}+22452257707354557240087211123792674816z^{32}}{z^{2}y^{8}(x^{2}y^{20}+7324992x^{2}y^{16}z^{4}-36178122424320x^{2}y^{12}z^{8}+31616122310661242880x^{2}y^{8}z^{12}+4658079989781080454463488x^{2}y^{4}z^{16}+14488079328898260609961820160x^{2}z^{20}-63504xy^{18}z^{3}+12093235200xy^{14}z^{7}+46167463635517440xy^{10}z^{11}+172517620199690273292288xy^{6}z^{15}+2817175663712377503794331648xy^{2}z^{19}-216y^{20}z^{2}+2052490752y^{16}z^{6}-2547148789776384y^{12}z^{10}+2396107307596552077312y^{8}z^{14}+67073076683666510642675712y^{4}z^{18}+7958661109946400884391936z^{22})}$ |
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 40.96.0-8.c.1.9 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 120.96.0-24.b.2.12 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-24.b.2.16 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-8.c.1.3 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-24.r.2.2 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-24.r.2.16 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-24.s.2.3 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-24.s.2.14 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.1-24.n.2.8 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.n.2.14 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.bi.1.8 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.bi.1.10 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.bj.1.4 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.bj.1.13 | $120$ | $2$ | $2$ | $1$ | $?$ | 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 |
|---|---|---|---|---|---|---|
| 120.384.5-24.be.1.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-24.bg.2.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-24.bh.1.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-24.bj.2.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.hl.2.15 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.hm.2.15 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.hq.2.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.hs.2.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-48.c.2.6 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-48.e.2.6 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-48.n.2.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-48.t.2.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-48.co.2.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-48.cu.2.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.cy.2.11 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.da.2.13 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-48.dd.2.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-48.df.2.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.fv.2.13 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.gb.1.13 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.ly.2.16 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.me.1.7 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.oz.2.15 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.pb.2.12 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |