Invariants
Level: | $24$ | $\SL_2$-level: | $24$ | Newform level: | $144$ | ||
Index: | $144$ | $\PSL_2$-index: | $144$ | ||||
Genus: | $8 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (none of which are rational) | Cusp widths | $12^{8}\cdot24^{2}$ | Cusp orbits | $2^{5}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | $0$ | ||||||
$\Q$-gonality: | $3 \le \gamma \le 6$ | ||||||
$\overline{\Q}$-gonality: | $3$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24A8 |
Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 24.144.8.26 |
Level structure
Jacobian
Conductor: | $2^{22}\cdot3^{16}$ |
Simple: | no |
Squarefree: | no |
Decomposition: | $1^{4}\cdot2^{2}$ |
Newforms: | 36.2.a.a$^{3}$, 72.2.d.a$^{2}$, 144.2.a.a |
Models
Canonical model in $\mathbb{P}^{ 7 }$ defined by 20 equations
$ 0 $ | $=$ | $ t v - u r $ |
$=$ | $x t + z t + w u$ | |
$=$ | $x u - z u - w t$ | |
$=$ | $x^{2} - z^{2} + w^{2}$ | |
$=$ | $\cdots$ |
Singular plane model Singular plane model
$ 0 $ | $=$ | $ 16 x^{6} y^{2} + 6 y^{6} z^{2} + 45 y^{4} z^{4} + 108 y^{2} z^{6} + 81 z^{8} $ |
Rational points
This modular curve has no real points, and therefore no rational points.
Maps between models of this curve
Birational map from canonical model to plane model:
$\displaystyle X$ | $=$ | $\displaystyle y$ |
$\displaystyle Y$ | $=$ | $\displaystyle z$ |
$\displaystyle Z$ | $=$ | $\displaystyle \frac{1}{3}t$ |
Maps to other modular curves
Map of degree 2 from the canonical model of this modular curve to the canonical model of the modular curve 12.72.4.b.1 :
$\displaystyle X$ | $=$ | $\displaystyle w$ |
$\displaystyle Y$ | $=$ | $\displaystyle z$ |
$\displaystyle Z$ | $=$ | $\displaystyle -x$ |
$\displaystyle W$ | $=$ | $\displaystyle -y$ |
Equation of the image curve:
$0$ | $=$ | $ X^{2}-Y^{2}+Z^{2} $ |
$=$ | $ XYZ+4W^{3} $ |
Modular covers
Cover information
Click on a modular curve in the diagram to see information about it.
|
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
12.72.4.b.1 | $12$ | $2$ | $2$ | $4$ | $0$ | $2^{2}$ |
24.48.0.c.1 | $24$ | $3$ | $3$ | $0$ | $0$ | full Jacobian |
24.72.4.y.1 | $24$ | $2$ | $2$ | $4$ | $0$ | $1^{2}\cdot2$ |
24.72.4.y.2 | $24$ | $2$ | $2$ | $4$ | $0$ | $1^{2}\cdot2$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
24.288.15.g.1 | $24$ | $2$ | $2$ | $15$ | $0$ | $1^{3}\cdot2^{2}$ |
24.288.15.k.1 | $24$ | $2$ | $2$ | $15$ | $2$ | $1^{3}\cdot2^{2}$ |
24.288.15.bg.1 | $24$ | $2$ | $2$ | $15$ | $0$ | $1^{3}\cdot2^{2}$ |
24.288.15.bl.1 | $24$ | $2$ | $2$ | $15$ | $0$ | $1^{3}\cdot2^{2}$ |
24.288.15.ci.1 | $24$ | $2$ | $2$ | $15$ | $0$ | $1^{3}\cdot2^{2}$ |
24.288.15.cm.1 | $24$ | $2$ | $2$ | $15$ | $0$ | $1^{3}\cdot2^{2}$ |
24.288.15.dg.1 | $24$ | $2$ | $2$ | $15$ | $1$ | $1^{3}\cdot2^{2}$ |
24.288.15.dk.1 | $24$ | $2$ | $2$ | $15$ | $0$ | $1^{3}\cdot2^{2}$ |
24.288.17.ok.1 | $24$ | $2$ | $2$ | $17$ | $1$ | $1^{5}\cdot2^{2}$ |
24.288.17.ok.2 | $24$ | $2$ | $2$ | $17$ | $1$ | $1^{5}\cdot2^{2}$ |
24.288.17.ol.1 | $24$ | $2$ | $2$ | $17$ | $1$ | $1^{5}\cdot2^{2}$ |
24.288.17.ol.2 | $24$ | $2$ | $2$ | $17$ | $1$ | $1^{5}\cdot2^{2}$ |
24.288.17.om.1 | $24$ | $2$ | $2$ | $17$ | $0$ | $1^{5}\cdot2^{2}$ |
24.288.17.om.2 | $24$ | $2$ | $2$ | $17$ | $0$ | $1^{5}\cdot2^{2}$ |
24.288.17.on.1 | $24$ | $2$ | $2$ | $17$ | $1$ | $1^{5}\cdot2^{2}$ |
24.288.17.on.2 | $24$ | $2$ | $2$ | $17$ | $1$ | $1^{5}\cdot2^{2}$ |
24.288.17.oo.1 | $24$ | $2$ | $2$ | $17$ | $1$ | $1^{5}\cdot2^{2}$ |
24.288.17.oo.2 | $24$ | $2$ | $2$ | $17$ | $1$ | $1^{5}\cdot2^{2}$ |
24.288.17.op.1 | $24$ | $2$ | $2$ | $17$ | $2$ | $1^{5}\cdot2^{2}$ |
24.288.17.op.2 | $24$ | $2$ | $2$ | $17$ | $2$ | $1^{5}\cdot2^{2}$ |
24.288.17.oq.1 | $24$ | $2$ | $2$ | $17$ | $2$ | $1^{5}\cdot2^{2}$ |
24.288.17.oq.2 | $24$ | $2$ | $2$ | $17$ | $2$ | $1^{5}\cdot2^{2}$ |
24.288.17.or.1 | $24$ | $2$ | $2$ | $17$ | $1$ | $1^{5}\cdot2^{2}$ |
24.288.17.or.2 | $24$ | $2$ | $2$ | $17$ | $1$ | $1^{5}\cdot2^{2}$ |
24.288.19.ep.1 | $24$ | $2$ | $2$ | $19$ | $2$ | $1^{5}\cdot2\cdot4$ |
24.288.19.eq.1 | $24$ | $2$ | $2$ | $19$ | $1$ | $1^{5}\cdot2\cdot4$ |
24.288.19.er.1 | $24$ | $2$ | $2$ | $19$ | $1$ | $1^{5}\cdot2\cdot4$ |
24.288.19.es.1 | $24$ | $2$ | $2$ | $19$ | $1$ | $1^{5}\cdot2\cdot4$ |
24.288.19.et.1 | $24$ | $2$ | $2$ | $19$ | $1$ | $1^{5}\cdot2\cdot4$ |
24.288.19.eu.1 | $24$ | $2$ | $2$ | $19$ | $2$ | $1^{5}\cdot2\cdot4$ |
24.288.19.ev.1 | $24$ | $2$ | $2$ | $19$ | $0$ | $1^{5}\cdot2\cdot4$ |
24.288.19.ew.1 | $24$ | $2$ | $2$ | $19$ | $1$ | $1^{5}\cdot2\cdot4$ |
120.288.15.dm.1 | $120$ | $2$ | $2$ | $15$ | $?$ | not computed |
120.288.15.dq.1 | $120$ | $2$ | $2$ | $15$ | $?$ | not computed |
120.288.15.fi.1 | $120$ | $2$ | $2$ | $15$ | $?$ | not computed |
120.288.15.fm.1 | $120$ | $2$ | $2$ | $15$ | $?$ | not computed |
120.288.15.he.1 | $120$ | $2$ | $2$ | $15$ | $?$ | not computed |
120.288.15.hi.1 | $120$ | $2$ | $2$ | $15$ | $?$ | not computed |
120.288.15.ja.1 | $120$ | $2$ | $2$ | $15$ | $?$ | not computed |
120.288.15.je.1 | $120$ | $2$ | $2$ | $15$ | $?$ | not computed |
120.288.17.bzg.1 | $120$ | $2$ | $2$ | $17$ | $?$ | not computed |
120.288.17.bzg.2 | $120$ | $2$ | $2$ | $17$ | $?$ | not computed |
120.288.17.bzh.1 | $120$ | $2$ | $2$ | $17$ | $?$ | not computed |
120.288.17.bzh.2 | $120$ | $2$ | $2$ | $17$ | $?$ | not computed |
120.288.17.bzi.1 | $120$ | $2$ | $2$ | $17$ | $?$ | not computed |
120.288.17.bzi.2 | $120$ | $2$ | $2$ | $17$ | $?$ | not computed |
120.288.17.bzj.1 | $120$ | $2$ | $2$ | $17$ | $?$ | not computed |
120.288.17.bzj.2 | $120$ | $2$ | $2$ | $17$ | $?$ | not computed |
120.288.17.bzk.1 | $120$ | $2$ | $2$ | $17$ | $?$ | not computed |
120.288.17.bzk.2 | $120$ | $2$ | $2$ | $17$ | $?$ | not computed |
120.288.17.bzl.1 | $120$ | $2$ | $2$ | $17$ | $?$ | not computed |
120.288.17.bzl.2 | $120$ | $2$ | $2$ | $17$ | $?$ | not computed |
120.288.17.bzm.1 | $120$ | $2$ | $2$ | $17$ | $?$ | not computed |
120.288.17.bzm.2 | $120$ | $2$ | $2$ | $17$ | $?$ | not computed |
120.288.17.bzn.1 | $120$ | $2$ | $2$ | $17$ | $?$ | not computed |
120.288.17.bzn.2 | $120$ | $2$ | $2$ | $17$ | $?$ | not computed |
120.288.19.po.1 | $120$ | $2$ | $2$ | $19$ | $?$ | not computed |
120.288.19.pp.1 | $120$ | $2$ | $2$ | $19$ | $?$ | not computed |
120.288.19.pq.1 | $120$ | $2$ | $2$ | $19$ | $?$ | not computed |
120.288.19.pr.1 | $120$ | $2$ | $2$ | $19$ | $?$ | not computed |
120.288.19.ps.1 | $120$ | $2$ | $2$ | $19$ | $?$ | not computed |
120.288.19.pt.1 | $120$ | $2$ | $2$ | $19$ | $?$ | not computed |
120.288.19.pu.1 | $120$ | $2$ | $2$ | $19$ | $?$ | not computed |
120.288.19.pv.1 | $120$ | $2$ | $2$ | $19$ | $?$ | not computed |
168.288.15.cu.1 | $168$ | $2$ | $2$ | $15$ | $?$ | not computed |
168.288.15.cy.1 | $168$ | $2$ | $2$ | $15$ | $?$ | not computed |
168.288.15.eq.1 | $168$ | $2$ | $2$ | $15$ | $?$ | not computed |
168.288.15.eu.1 | $168$ | $2$ | $2$ | $15$ | $?$ | not computed |
168.288.15.gm.1 | $168$ | $2$ | $2$ | $15$ | $?$ | not computed |
168.288.15.gq.1 | $168$ | $2$ | $2$ | $15$ | $?$ | not computed |
168.288.15.ii.1 | $168$ | $2$ | $2$ | $15$ | $?$ | not computed |
168.288.15.im.1 | $168$ | $2$ | $2$ | $15$ | $?$ | not computed |
168.288.17.bvo.1 | $168$ | $2$ | $2$ | $17$ | $?$ | not computed |
168.288.17.bvo.2 | $168$ | $2$ | $2$ | $17$ | $?$ | not computed |
168.288.17.bvp.1 | $168$ | $2$ | $2$ | $17$ | $?$ | not computed |
168.288.17.bvp.2 | $168$ | $2$ | $2$ | $17$ | $?$ | not computed |
168.288.17.bvq.1 | $168$ | $2$ | $2$ | $17$ | $?$ | not computed |
168.288.17.bvq.2 | $168$ | $2$ | $2$ | $17$ | $?$ | not computed |
168.288.17.bvr.1 | $168$ | $2$ | $2$ | $17$ | $?$ | not computed |
168.288.17.bvr.2 | $168$ | $2$ | $2$ | $17$ | $?$ | not computed |
168.288.17.bvs.1 | $168$ | $2$ | $2$ | $17$ | $?$ | not computed |
168.288.17.bvs.2 | $168$ | $2$ | $2$ | $17$ | $?$ | not computed |
168.288.17.bvt.1 | $168$ | $2$ | $2$ | $17$ | $?$ | not computed |
168.288.17.bvt.2 | $168$ | $2$ | $2$ | $17$ | $?$ | not computed |
168.288.17.bvu.1 | $168$ | $2$ | $2$ | $17$ | $?$ | not computed |
168.288.17.bvu.2 | $168$ | $2$ | $2$ | $17$ | $?$ | not computed |
168.288.17.bvv.1 | $168$ | $2$ | $2$ | $17$ | $?$ | not computed |
168.288.17.bvv.2 | $168$ | $2$ | $2$ | $17$ | $?$ | not computed |
168.288.19.of.1 | $168$ | $2$ | $2$ | $19$ | $?$ | not computed |
168.288.19.og.1 | $168$ | $2$ | $2$ | $19$ | $?$ | not computed |
168.288.19.oh.1 | $168$ | $2$ | $2$ | $19$ | $?$ | not computed |
168.288.19.oi.1 | $168$ | $2$ | $2$ | $19$ | $?$ | not computed |
168.288.19.oj.1 | $168$ | $2$ | $2$ | $19$ | $?$ | not computed |
168.288.19.ok.1 | $168$ | $2$ | $2$ | $19$ | $?$ | not computed |
168.288.19.ol.1 | $168$ | $2$ | $2$ | $19$ | $?$ | not computed |
168.288.19.om.1 | $168$ | $2$ | $2$ | $19$ | $?$ | not computed |
264.288.15.cu.1 | $264$ | $2$ | $2$ | $15$ | $?$ | not computed |
264.288.15.cy.1 | $264$ | $2$ | $2$ | $15$ | $?$ | not computed |
264.288.15.eq.1 | $264$ | $2$ | $2$ | $15$ | $?$ | not computed |
264.288.15.eu.1 | $264$ | $2$ | $2$ | $15$ | $?$ | not computed |
264.288.15.gm.1 | $264$ | $2$ | $2$ | $15$ | $?$ | not computed |
264.288.15.gq.1 | $264$ | $2$ | $2$ | $15$ | $?$ | not computed |
264.288.15.ii.1 | $264$ | $2$ | $2$ | $15$ | $?$ | not computed |
264.288.15.im.1 | $264$ | $2$ | $2$ | $15$ | $?$ | not computed |
264.288.17.bvo.1 | $264$ | $2$ | $2$ | $17$ | $?$ | not computed |
264.288.17.bvo.2 | $264$ | $2$ | $2$ | $17$ | $?$ | not computed |
264.288.17.bvp.1 | $264$ | $2$ | $2$ | $17$ | $?$ | not computed |
264.288.17.bvp.2 | $264$ | $2$ | $2$ | $17$ | $?$ | not computed |
264.288.17.bvq.1 | $264$ | $2$ | $2$ | $17$ | $?$ | not computed |
264.288.17.bvq.2 | $264$ | $2$ | $2$ | $17$ | $?$ | not computed |
264.288.17.bvr.1 | $264$ | $2$ | $2$ | $17$ | $?$ | not computed |
264.288.17.bvr.2 | $264$ | $2$ | $2$ | $17$ | $?$ | not computed |
264.288.17.bvs.1 | $264$ | $2$ | $2$ | $17$ | $?$ | not computed |
264.288.17.bvs.2 | $264$ | $2$ | $2$ | $17$ | $?$ | not computed |
264.288.17.bvt.1 | $264$ | $2$ | $2$ | $17$ | $?$ | not computed |
264.288.17.bvt.2 | $264$ | $2$ | $2$ | $17$ | $?$ | not computed |
264.288.17.bvu.1 | $264$ | $2$ | $2$ | $17$ | $?$ | not computed |
264.288.17.bvu.2 | $264$ | $2$ | $2$ | $17$ | $?$ | not computed |
264.288.17.bvv.1 | $264$ | $2$ | $2$ | $17$ | $?$ | not computed |
264.288.17.bvv.2 | $264$ | $2$ | $2$ | $17$ | $?$ | not computed |
264.288.19.of.1 | $264$ | $2$ | $2$ | $19$ | $?$ | not computed |
264.288.19.og.1 | $264$ | $2$ | $2$ | $19$ | $?$ | not computed |
264.288.19.oh.1 | $264$ | $2$ | $2$ | $19$ | $?$ | not computed |
264.288.19.oi.1 | $264$ | $2$ | $2$ | $19$ | $?$ | not computed |
264.288.19.oj.1 | $264$ | $2$ | $2$ | $19$ | $?$ | not computed |
264.288.19.ok.1 | $264$ | $2$ | $2$ | $19$ | $?$ | not computed |
264.288.19.ol.1 | $264$ | $2$ | $2$ | $19$ | $?$ | not computed |
264.288.19.om.1 | $264$ | $2$ | $2$ | $19$ | $?$ | not computed |
312.288.15.cu.1 | $312$ | $2$ | $2$ | $15$ | $?$ | not computed |
312.288.15.cy.1 | $312$ | $2$ | $2$ | $15$ | $?$ | not computed |
312.288.15.eq.1 | $312$ | $2$ | $2$ | $15$ | $?$ | not computed |
312.288.15.eu.1 | $312$ | $2$ | $2$ | $15$ | $?$ | not computed |
312.288.15.gm.1 | $312$ | $2$ | $2$ | $15$ | $?$ | not computed |
312.288.15.gq.1 | $312$ | $2$ | $2$ | $15$ | $?$ | not computed |
312.288.15.ii.1 | $312$ | $2$ | $2$ | $15$ | $?$ | not computed |
312.288.15.im.1 | $312$ | $2$ | $2$ | $15$ | $?$ | not computed |
312.288.17.bvo.1 | $312$ | $2$ | $2$ | $17$ | $?$ | not computed |
312.288.17.bvo.2 | $312$ | $2$ | $2$ | $17$ | $?$ | not computed |
312.288.17.bvp.1 | $312$ | $2$ | $2$ | $17$ | $?$ | not computed |
312.288.17.bvp.2 | $312$ | $2$ | $2$ | $17$ | $?$ | not computed |
312.288.17.bvq.1 | $312$ | $2$ | $2$ | $17$ | $?$ | not computed |
312.288.17.bvq.2 | $312$ | $2$ | $2$ | $17$ | $?$ | not computed |
312.288.17.bvr.1 | $312$ | $2$ | $2$ | $17$ | $?$ | not computed |
312.288.17.bvr.2 | $312$ | $2$ | $2$ | $17$ | $?$ | not computed |
312.288.17.bvs.1 | $312$ | $2$ | $2$ | $17$ | $?$ | not computed |
312.288.17.bvs.2 | $312$ | $2$ | $2$ | $17$ | $?$ | not computed |
312.288.17.bvt.1 | $312$ | $2$ | $2$ | $17$ | $?$ | not computed |
312.288.17.bvt.2 | $312$ | $2$ | $2$ | $17$ | $?$ | not computed |
312.288.17.bvu.1 | $312$ | $2$ | $2$ | $17$ | $?$ | not computed |
312.288.17.bvu.2 | $312$ | $2$ | $2$ | $17$ | $?$ | not computed |
312.288.17.bvv.1 | $312$ | $2$ | $2$ | $17$ | $?$ | not computed |
312.288.17.bvv.2 | $312$ | $2$ | $2$ | $17$ | $?$ | not computed |
312.288.19.pl.1 | $312$ | $2$ | $2$ | $19$ | $?$ | not computed |
312.288.19.pm.1 | $312$ | $2$ | $2$ | $19$ | $?$ | not computed |
312.288.19.pn.1 | $312$ | $2$ | $2$ | $19$ | $?$ | not computed |
312.288.19.po.1 | $312$ | $2$ | $2$ | $19$ | $?$ | not computed |
312.288.19.pp.1 | $312$ | $2$ | $2$ | $19$ | $?$ | not computed |
312.288.19.pq.1 | $312$ | $2$ | $2$ | $19$ | $?$ | not computed |
312.288.19.pr.1 | $312$ | $2$ | $2$ | $19$ | $?$ | not computed |
312.288.19.ps.1 | $312$ | $2$ | $2$ | $19$ | $?$ | not computed |