↑

Properties

Label 60.2880.101-60.d.1.24
Level $60$
Index $2880$
Genus $101$
Analytic rank $7$
Cusps $40$
$\Q$-cusps $0$

Related objects

Downloads

Learn more

Invariants

Level: $60$ $\SL_2$-level: $60$ Newform level: $900$
Index: $2880$ $\PSL_2$-index:$1440$
Genus: $101 = 1 + \frac{ 1440 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 40 }{2}$
Cusps: $40$ (none of which are rational) Cusp widths $30^{32}\cdot60^{8}$ Cusp orbits $2^{4}\cdot4^{6}\cdot8$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: $7$
$\Q$-gonality: $15 \le \gamma \le 30$
$\overline{\Q}$-gonality: $15 \le \gamma \le 30$
Rational cusps: $0$
Rational CM points: none

Other labels

Rouse, Sutherland, and Zureick-Brown (RSZB) label: 60.2880.101.24

Level structure

$\GL_2(\Z/60\Z)$-generators: $\begin{bmatrix}13&24\\36&37\end{bmatrix}$, $\begin{bmatrix}17&14\\18&13\end{bmatrix}$, $\begin{bmatrix}41&54\\0&59\end{bmatrix}$, $\begin{bmatrix}43&4\\48&35\end{bmatrix}$, $\begin{bmatrix}43&52\\30&47\end{bmatrix}$, $\begin{bmatrix}49&40\\42&11\end{bmatrix}$
$\GL_2(\Z/60\Z)$-subgroup: $C_{24}:C_2^5$
Contains $-I$: no $\quad$ (see 60.1440.101.d.1 for the level structure with $-I$)
Cyclic 60-isogeny field degree: $12$
Cyclic 60-torsion field degree: $96$
Full 60-torsion field degree: $768$

Jacobian

Conductor: $2^{142}\cdot3^{134}\cdot5^{196}$
Simple: no
Squarefree: no
Decomposition: $1^{49}\cdot2^{2}\cdot8^{6}$
Newforms: 36.2.a.a, 36.2.b.a, 50.2.a.b$^{6}$, 75.2.a.a$^{6}$, 75.2.a.b$^{6}$, 100.2.a.a$^{3}$, 150.2.a.b$^{4}$, 225.2.a.b$^{3}$, 225.2.a.c$^{3}$, 225.2.a.e$^{3}$, 300.2.a.b$^{2}$, 300.2.e.c$^{2}$, 300.2.e.e$^{2}$, 450.2.a.a$^{2}$, 450.2.a.c$^{2}$, 450.2.a.d$^{2}$, 450.2.a.e$^{2}$, 900.2.a.b, 900.2.a.e, 900.2.a.f, 900.2.a.g, 900.2.e.b, 900.2.e.d, 900.2.e.g

Rational points

This modular curve has no $\Q_p$ points for $p=7,13,37,53,103,367$, and therefore no rational points.

Modular covers

The following modular covers realize this modular curve as a fiber product over $X(1)$.

Factor curve Level Index Degree Genus Rank Kernel decomposition
$X_{\mathrm{ns}}^+(5)$ $5$ $288$ $144$ $0$ $0$ full Jacobian
12.288.3-12.a.1.13 $12$ $10$ $10$ $3$ $0$ $1^{48}\cdot2\cdot8^{6}$

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank Kernel decomposition
12.288.3-12.a.1.13 $12$ $10$ $10$ $3$ $0$ $1^{48}\cdot2\cdot8^{6}$
60.960.31-60.a.1.24 $60$ $3$ $3$ $31$ $0$ $1^{34}\cdot2^{2}\cdot8^{4}$
60.960.31-60.a.2.7 $60$ $3$ $3$ $31$ $0$ $1^{34}\cdot2^{2}\cdot8^{4}$
60.1440.49-30.a.1.11 $60$ $2$ $2$ $49$ $7$ $2^{2}\cdot8^{6}$
60.1440.49-30.a.1.18 $60$ $2$ $2$ $49$ $7$ $2^{2}\cdot8^{6}$

This modular curve is minimally covered by the modular curves in the database listed below.

Covering curve Level Index Degree Genus Rank Kernel decomposition
60.5760.201-60.c.1.12 $60$ $2$ $2$ $201$ $15$ $1^{42}\cdot2^{5}\cdot4^{4}\cdot8^{4}$
60.5760.201-60.d.1.19 $60$ $2$ $2$ $201$ $31$ $1^{42}\cdot2^{5}\cdot4^{4}\cdot8^{4}$
60.5760.201-60.g.1.13 $60$ $2$ $2$ $201$ $15$ $1^{42}\cdot2^{5}\cdot4^{4}\cdot8^{4}$
60.5760.201-60.h.1.12 $60$ $2$ $2$ $201$ $27$ $1^{42}\cdot2^{5}\cdot4^{4}\cdot8^{4}$
60.5760.201-60.k.1.20 $60$ $2$ $2$ $201$ $31$ $1^{42}\cdot2^{5}\cdot4^{4}\cdot8^{4}$
60.5760.201-60.l.1.14 $60$ $2$ $2$ $201$ $17$ $1^{42}\cdot2^{5}\cdot4^{4}\cdot8^{4}$
60.5760.201-60.o.1.11 $60$ $2$ $2$ $201$ $23$ $1^{42}\cdot2^{5}\cdot4^{4}\cdot8^{4}$
60.5760.201-60.p.1.27 $60$ $2$ $2$ $201$ $19$ $1^{42}\cdot2^{5}\cdot4^{4}\cdot8^{4}$
60.5760.209-60.cs.1.11 $60$ $2$ $2$ $209$ $29$ $1^{56}\cdot2^{2}\cdot8^{6}$
60.5760.209-60.cs.1.22 $60$ $2$ $2$ $209$ $29$ $1^{56}\cdot2^{2}\cdot8^{6}$
60.5760.209-60.ct.1.20 $60$ $2$ $2$ $209$ $20$ $1^{56}\cdot2^{2}\cdot8^{6}$
60.5760.209-60.ct.2.4 $60$ $2$ $2$ $209$ $20$ $1^{56}\cdot2^{2}\cdot8^{6}$
60.5760.209-60.cw.1.18 $60$ $2$ $2$ $209$ $25$ $1^{56}\cdot2^{2}\cdot8^{6}$
60.5760.209-60.cw.2.5 $60$ $2$ $2$ $209$ $25$ $1^{56}\cdot2^{2}\cdot8^{6}$
60.5760.209-60.cx.1.3 $60$ $2$ $2$ $209$ $15$ $1^{56}\cdot2^{2}\cdot8^{6}$
60.5760.209-60.cx.2.27 $60$ $2$ $2$ $209$ $15$ $1^{56}\cdot2^{2}\cdot8^{6}$
60.5760.209-60.da.1.20 $60$ $2$ $2$ $209$ $33$ $1^{54}\cdot2^{3}\cdot4^{4}\cdot8^{4}$
60.5760.209-60.da.2.8 $60$ $2$ $2$ $209$ $33$ $1^{54}\cdot2^{3}\cdot4^{4}\cdot8^{4}$
60.5760.209-60.db.1.17 $60$ $2$ $2$ $209$ $25$ $1^{54}\cdot2^{3}\cdot4^{4}\cdot8^{4}$
60.5760.209-60.db.2.6 $60$ $2$ $2$ $209$ $25$ $1^{54}\cdot2^{3}\cdot4^{4}\cdot8^{4}$
60.5760.209-60.de.1.17 $60$ $2$ $2$ $209$ $33$ $1^{54}\cdot2^{3}\cdot4^{4}\cdot8^{4}$
60.5760.209-60.de.2.6 $60$ $2$ $2$ $209$ $33$ $1^{54}\cdot2^{3}\cdot4^{4}\cdot8^{4}$
60.5760.209-60.df.1.8 $60$ $2$ $2$ $209$ $25$ $1^{54}\cdot2^{3}\cdot4^{4}\cdot8^{4}$
60.5760.209-60.df.2.18 $60$ $2$ $2$ $209$ $25$ $1^{54}\cdot2^{3}\cdot4^{4}\cdot8^{4}$
60.5760.209-60.eo.1.6 $60$ $2$ $2$ $209$ $23$ $1^{54}\cdot2^{3}\cdot4^{4}\cdot8^{4}$
60.5760.209-60.eo.2.19 $60$ $2$ $2$ $209$ $23$ $1^{54}\cdot2^{3}\cdot4^{4}\cdot8^{4}$
60.5760.209-60.ep.1.17 $60$ $2$ $2$ $209$ $29$ $1^{54}\cdot2^{3}\cdot4^{4}\cdot8^{4}$
60.5760.209-60.ep.2.8 $60$ $2$ $2$ $209$ $29$ $1^{54}\cdot2^{3}\cdot4^{4}\cdot8^{4}$
60.5760.209-60.es.1.18 $60$ $2$ $2$ $209$ $23$ $1^{54}\cdot2^{3}\cdot4^{4}\cdot8^{4}$
60.5760.209-60.es.2.8 $60$ $2$ $2$ $209$ $23$ $1^{54}\cdot2^{3}\cdot4^{4}\cdot8^{4}$
60.5760.209-60.et.1.7 $60$ $2$ $2$ $209$ $29$ $1^{54}\cdot2^{3}\cdot4^{4}\cdot8^{4}$
60.5760.209-60.et.2.18 $60$ $2$ $2$ $209$ $29$ $1^{54}\cdot2^{3}\cdot4^{4}\cdot8^{4}$
60.5760.209-60.ew.1.7 $60$ $2$ $2$ $209$ $19$ $1^{56}\cdot2^{2}\cdot8^{6}$
60.5760.209-60.ew.2.28 $60$ $2$ $2$ $209$ $19$ $1^{56}\cdot2^{2}\cdot8^{6}$
60.5760.209-60.ex.1.19 $60$ $2$ $2$ $209$ $26$ $1^{56}\cdot2^{2}\cdot8^{6}$
60.5760.209-60.ex.2.12 $60$ $2$ $2$ $209$ $26$ $1^{56}\cdot2^{2}\cdot8^{6}$
60.5760.209-60.fe.1.11 $60$ $2$ $2$ $209$ $24$ $1^{56}\cdot2^{2}\cdot8^{6}$
60.5760.209-60.fe.2.2 $60$ $2$ $2$ $209$ $24$ $1^{56}\cdot2^{2}\cdot8^{6}$
60.5760.209-60.ff.1.5 $60$ $2$ $2$ $209$ $30$ $1^{56}\cdot2^{2}\cdot8^{6}$
60.5760.209-60.ff.1.24 $60$ $2$ $2$ $209$ $30$ $1^{56}\cdot2^{2}\cdot8^{6}$
60.5760.217-60.mu.1.6 $60$ $2$ $2$ $217$ $29$ $1^{56}\cdot2^{14}\cdot4^{6}\cdot8$
60.5760.217-60.mv.1.6 $60$ $2$ $2$ $217$ $20$ $1^{56}\cdot2^{14}\cdot4^{6}\cdot8$
60.5760.217-60.ne.1.7 $60$ $2$ $2$ $217$ $25$ $1^{56}\cdot2^{14}\cdot4^{6}\cdot8$
60.5760.217-60.nf.1.5 $60$ $2$ $2$ $217$ $15$ $1^{56}\cdot2^{14}\cdot4^{6}\cdot8$
60.5760.217-60.nq.1.13 $60$ $2$ $2$ $217$ $33$ $1^{54}\cdot2^{11}\cdot4^{10}$
60.5760.217-60.nr.1.11 $60$ $2$ $2$ $217$ $25$ $1^{54}\cdot2^{11}\cdot4^{10}$
60.5760.217-60.nw.1.12 $60$ $2$ $2$ $217$ $33$ $1^{54}\cdot2^{11}\cdot4^{10}$
60.5760.217-60.nx.1.10 $60$ $2$ $2$ $217$ $25$ $1^{54}\cdot2^{11}\cdot4^{10}$
60.5760.217-60.ps.1.11 $60$ $2$ $2$ $217$ $23$ $1^{54}\cdot2^{11}\cdot4^{10}$
60.5760.217-60.pt.1.13 $60$ $2$ $2$ $217$ $29$ $1^{54}\cdot2^{11}\cdot4^{10}$
60.5760.217-60.qc.1.10 $60$ $2$ $2$ $217$ $23$ $1^{54}\cdot2^{11}\cdot4^{10}$
60.5760.217-60.qd.1.12 $60$ $2$ $2$ $217$ $29$ $1^{54}\cdot2^{11}\cdot4^{10}$
60.5760.217-60.qu.1.6 $60$ $2$ $2$ $217$ $19$ $1^{56}\cdot2^{14}\cdot4^{6}\cdot8$
60.5760.217-60.qv.1.6 $60$ $2$ $2$ $217$ $26$ $1^{56}\cdot2^{14}\cdot4^{6}\cdot8$
60.5760.217-60.sg.1.5 $60$ $2$ $2$ $217$ $24$ $1^{56}\cdot2^{14}\cdot4^{6}\cdot8$
60.5760.217-60.sh.1.7 $60$ $2$ $2$ $217$ $30$ $1^{56}\cdot2^{14}\cdot4^{6}\cdot8$
60.8640.301-60.i.1.33 $60$ $3$ $3$ $301$ $18$ $1^{90}\cdot2^{7}\cdot4^{4}\cdot8^{10}$