↑

Properties

Label 63.24.0.c.1
Level $63$
Index $24$
Genus $0$
Analytic rank $0$
Cusps $6$
$\Q$-cusps $0$

Related objects

Downloads

Learn more

Invariants

Level: $63$ $\SL_2$-level: $7$
Index: $24$ $\PSL_2$-index:$24$
Genus: $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$
Cusps: $6$ (none of which are rational) Cusp widths $1^{3}\cdot7^{3}$ Cusp orbits $3^{2}$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
$\Q$-gonality: $1 \le \gamma \le 2$
$\overline{\Q}$-gonality: $1$
Rational cusps: $0$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 7E0
Rouse, Sutherland, and Zureick-Brown (RSZB) label: 63.24.0.2

Level structure

$\GL_2(\Z/63\Z)$-generators: $\begin{bmatrix}12&62\\14&18\end{bmatrix}$, $\begin{bmatrix}40&22\\35&45\end{bmatrix}$, $\begin{bmatrix}47&23\\49&20\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 63.48.0-63.c.1.1, 63.48.0-63.c.1.2, 63.48.0-63.c.1.3, 63.48.0-63.c.1.4, 126.48.0-63.c.1.1, 126.48.0-63.c.1.2, 126.48.0-63.c.1.3, 126.48.0-63.c.1.4, 252.48.0-63.c.1.1, 252.48.0-63.c.1.2, 252.48.0-63.c.1.3, 252.48.0-63.c.1.4, 252.48.0-63.c.1.5, 252.48.0-63.c.1.6, 252.48.0-63.c.1.7, 252.48.0-63.c.1.8, 315.48.0-63.c.1.1, 315.48.0-63.c.1.2, 315.48.0-63.c.1.3, 315.48.0-63.c.1.4
Cyclic 63-isogeny field degree: $12$
Cyclic 63-torsion field degree: $432$
Full 63-torsion field degree: $326592$

Models

This modular curve is isomorphic to $\mathbb{P}^1$.

Rational points

This modular curve has infinitely many rational points, including 7 stored non-cuspidal points.

Maps to other modular curves

$j$-invariant map of degree 24 to the modular curve $X(1)$ :

$\displaystyle j$ $=$ $\displaystyle \frac{3^2\cdot7^5}{2}\cdot\frac{(x+2y)^{24}(4x^{2}-2xy+7y^{2})^{3}(1088x^{6}+672x^{5}y-188160x^{4}y^{2}+174440x^{3}y^{3}+164640x^{2}y^{4}-96726xy^{5}-43561y^{6})^{3}}{(x+2y)^{24}(40x^{3}+168x^{2}y-294xy^{2}-49y^{3})^{7}(64x^{3}+798x^{2}y-735xy^{2}-343y^{3})}$

Modular covers

Sorry, your browser does not support the nearby lattice.

Cover information

Click on a modular curve in the diagram to see information about it.
See a full page version of the diagram

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank
$X_0(7)$ $7$ $3$ $3$ $0$ $0$

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

Covering curve Level Index Degree Genus
63.72.4.c.2 $63$ $3$ $3$ $4$
63.96.3.c.2 $63$ $4$ $4$ $3$
63.168.3.a.1 $63$ $7$ $7$ $3$
63.648.46.e.2 $63$ $27$ $27$ $46$
126.48.2.f.1 $126$ $2$ $2$ $2$
126.48.2.g.1 $126$ $2$ $2$ $2$
126.48.2.n.1 $126$ $2$ $2$ $2$
126.48.2.o.1 $126$ $2$ $2$ $2$
126.72.1.m.2 $126$ $3$ $3$ $1$
252.48.2.m.2 $252$ $2$ $2$ $2$
252.48.2.n.2 $252$ $2$ $2$ $2$
252.48.2.u.2 $252$ $2$ $2$ $2$
252.48.2.v.2 $252$ $2$ $2$ $2$
252.96.6.bm.2 $252$ $4$ $4$ $6$
315.120.8.c.2 $315$ $5$ $5$ $8$
315.144.7.k.1 $315$ $6$ $6$ $7$
315.240.15.g.1 $315$ $10$ $10$ $15$