Invariants
| Level: | $120$ | $\SL_2$-level: | $8$ | Newform level: | $288$ | ||
| 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: | $\begin{bmatrix}5&116\\66&71\end{bmatrix}$, $\begin{bmatrix}13&36\\78&67\end{bmatrix}$, $\begin{bmatrix}45&104\\74&89\end{bmatrix}$, $\begin{bmatrix}67&8\\62&87\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 24.96.1.cd.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $24$ |
| Cyclic 120-torsion field degree: | $768$ |
| Full 120-torsion field degree: | $184320$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | 288.2.a.d |
Models
Weierstrass model Weierstrass model
| $ y^{2} $ | $=$ | $ x^{3} - 9x $ |
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 $X(1)$ :
| $\displaystyle j$ | $=$ | $\displaystyle -\frac{1}{3^2}\cdot\frac{14112468x^{2}y^{28}z^{2}+178127386413570x^{2}y^{24}z^{6}+6962494991310477351x^{2}y^{20}z^{10}+18041756667105025196595x^{2}y^{16}z^{14}+6231353476666506100422264x^{2}y^{12}z^{18}+583688060519941241389549485x^{2}y^{8}z^{22}+18357451653402196690396589541x^{2}y^{4}z^{26}+148695418365105736174136457735x^{2}z^{30}+6408xy^{30}z+2130754467186xy^{26}z^{5}+320818616388124488xy^{22}z^{9}+2052468590721326777817xy^{18}z^{13}+1518782811917983115962176xy^{14}z^{17}+234621485135854096045521465xy^{10}z^{21}+11898354747565875333902679900xy^{6}z^{25}+181738856485713392638390465137xy^{2}z^{29}+y^{32}+11567427912y^{28}z^{4}+8380519155108828y^{24}z^{8}+105003536964696697806y^{20}z^{12}+112831932610271871984924y^{16}z^{16}+20147482624549642972232976y^{12}z^{20}+1118092516920807220810928286y^{8}z^{24}+18357536526064766366816549322y^{4}z^{28}+79766443076872509863361z^{32}}{zy^{4}(279x^{2}y^{24}z-6547878x^{2}y^{20}z^{5}+928402980714x^{2}y^{16}z^{9}+6384365000350218x^{2}y^{12}z^{13}-35480743464960964647x^{2}y^{8}z^{17}-51490437158783705678505x^{2}y^{4}z^{21}-1416469339858957679723175x^{2}z^{25}-xy^{26}+1283040xy^{22}z^{4}+28807290846xy^{18}z^{8}-557233088056524xy^{14}z^{12}+1462069079984772117xy^{10}z^{16}-9823100501945895691032xy^{6}z^{20}-1416470840805310649714385xy^{2}z^{24}-30780y^{24}z^{3}-1575191124y^{20}z^{7}-25763936032431y^{16}z^{11}+189348669283883868y^{12}z^{15}-623704633846772918040y^{8}z^{19}-139897639381645192050054y^{4}z^{23}-12157665459056928801z^{27})}$ |
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.l.1.3 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 120.96.0-24.i.2.7 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-24.i.2.14 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-24.j.2.1 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-24.j.2.9 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-8.l.1.2 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-24.bb.1.7 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-24.bb.1.11 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.1-24.be.2.11 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.be.2.16 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.bf.2.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.bf.2.14 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.bu.1.6 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.bu.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 |
|---|---|---|---|---|---|---|
| 240.384.5-48.bq.1.4 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-48.cb.1.4 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-48.dj.1.11 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-48.dk.1.9 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-48.dn.1.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-48.do.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-48.dr.1.9 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-48.ds.1.10 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-48.dv.1.9 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-48.dw.1.10 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-48.ef.1.4 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-48.ek.1.4 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.sx.1.7 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.tf.1.7 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.uv.2.19 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.uw.1.26 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.vh.1.10 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.vi.1.2 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.vl.1.25 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.vm.2.25 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.vx.1.17 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.vy.1.21 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.xf.1.6 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.xn.1.6 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |