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Properties

Label 252.216.10.bv.1
Level $252$
Index $216$
Genus $10$
Cusps $18$
$\Q$-cusps $2$

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Invariants

Level: $252$ $\SL_2$-level: $36$ Newform level: $1$
Index: $216$ $\PSL_2$-index:$216$
Genus: $10 = 1 + \frac{ 216 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 18 }{2}$
Cusps: $18$ (of which $2$ are rational) Cusp widths $3^{6}\cdot9^{6}\cdot12^{3}\cdot36^{3}$ Cusp orbits $1^{2}\cdot2^{4}\cdot4^{2}$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: not computed
$\Q$-gonality: $4 \le \gamma \le 10$
$\overline{\Q}$-gonality: $4 \le \gamma \le 10$
Rational cusps: $2$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 36Q10

Level structure

$\GL_2(\Z/252\Z)$-generators: $\begin{bmatrix}71&193\\18&211\end{bmatrix}$, $\begin{bmatrix}149&184\\180&163\end{bmatrix}$, $\begin{bmatrix}211&246\\90&19\end{bmatrix}$, $\begin{bmatrix}215&103\\12&79\end{bmatrix}$, $\begin{bmatrix}217&233\\48&23\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 252.432.10-252.bv.1.1, 252.432.10-252.bv.1.2, 252.432.10-252.bv.1.3, 252.432.10-252.bv.1.4, 252.432.10-252.bv.1.5, 252.432.10-252.bv.1.6, 252.432.10-252.bv.1.7, 252.432.10-252.bv.1.8, 252.432.10-252.bv.1.9, 252.432.10-252.bv.1.10, 252.432.10-252.bv.1.11, 252.432.10-252.bv.1.12, 252.432.10-252.bv.1.13, 252.432.10-252.bv.1.14, 252.432.10-252.bv.1.15, 252.432.10-252.bv.1.16
Cyclic 252-isogeny field degree: $16$
Cyclic 252-torsion field degree: $1152$
Full 252-torsion field degree: $3483648$

Rational points

This modular curve has 2 rational cusps but no known non-cuspidal rational points.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank
18.108.4.c.1 $18$ $2$ $2$ $4$ $0$
84.72.1.r.1 $84$ $3$ $3$ $1$ $?$
252.72.1.j.1 $252$ $3$ $3$ $1$ $?$
252.72.4.w.1 $252$ $3$ $3$ $4$ $?$
252.72.4.be.1 $252$ $3$ $3$ $4$ $?$