↑

Properties

Label 114.24.0.b.1
Level $114$
Index $24$
Genus $0$
Cusps $6$
$\Q$-cusps $2$

Related objects

Downloads

Learn more

Invariants

Level: $114$ $\SL_2$-level: $6$
Index: $24$ $\PSL_2$-index:$24$
Genus: $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$
Cusps: $6$ (of which $2$ are rational) Cusp widths $2^{3}\cdot6^{3}$ Cusp orbits $1^{2}\cdot2^{2}$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
$\Q$-gonality: $1$
$\overline{\Q}$-gonality: $1$
Rational cusps: $2$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 6I0

Level structure

$\GL_2(\Z/114\Z)$-generators: $\begin{bmatrix}2&15\\83&40\end{bmatrix}$, $\begin{bmatrix}57&104\\86&75\end{bmatrix}$, $\begin{bmatrix}101&60\\44&61\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 114.48.0-114.b.1.1, 114.48.0-114.b.1.2, 114.48.0-114.b.1.3, 114.48.0-114.b.1.4, 228.48.0-114.b.1.1, 228.48.0-114.b.1.2, 228.48.0-114.b.1.3, 228.48.0-114.b.1.4, 228.48.0-114.b.1.5, 228.48.0-114.b.1.6, 228.48.0-114.b.1.7, 228.48.0-114.b.1.8, 228.48.0-114.b.1.9, 228.48.0-114.b.1.10, 228.48.0-114.b.1.11, 228.48.0-114.b.1.12
Cyclic 114-isogeny field degree: $20$
Cyclic 114-torsion field degree: $720$
Full 114-torsion field degree: $1477440$

Models

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

Rational points

This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.

Modular covers

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

Factor curve Level Index Degree Genus Rank
$X_0(3)$ $3$ $6$ $6$ $0$ $0$
38.6.0.b.1 $38$ $4$ $4$ $0$ $0$

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank
$X_0(6)$ $6$ $2$ $2$ $0$ $0$
38.6.0.b.1 $38$ $4$ $4$ $0$ $0$
114.8.0.a.1 $114$ $3$ $3$ $0$ $?$

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

Covering curve Level Index Degree Genus
114.72.1.d.1 $114$ $3$ $3$ $1$
228.48.1.i.1 $228$ $2$ $2$ $1$
228.48.1.k.1 $228$ $2$ $2$ $1$
228.48.1.u.1 $228$ $2$ $2$ $1$
228.48.1.w.1 $228$ $2$ $2$ $1$
228.48.1.bg.1 $228$ $2$ $2$ $1$
228.48.1.bi.1 $228$ $2$ $2$ $1$
228.48.1.bo.1 $228$ $2$ $2$ $1$
228.48.1.bq.1 $228$ $2$ $2$ $1$