Properties

Label 114.36.1.o.1
Level $114$
Index $36$
Genus $1$
Cusps $6$
$\Q$-cusps $0$

Related objects

Downloads

Learn more

Invariants

Level: $114$ $\SL_2$-level: $6$ Newform level: $1$
Index: $36$ $\PSL_2$-index:$36$
Genus: $1 = 1 + \frac{ 36 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$
Cusps: $6$ (none of which are rational) Cusp widths $6^{6}$ Cusp orbits $2\cdot4$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: not computed
$\Q$-gonality: $2 \le \gamma \le 36$
$\overline{\Q}$-gonality: $2$
Rational cusps: $0$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 6E1

Level structure

$\GL_2(\Z/114\Z)$-generators: $\begin{bmatrix}57&86\\79&111\end{bmatrix}$, $\begin{bmatrix}65&62\\74&111\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: none in database
Cyclic 114-isogeny field degree: $80$
Cyclic 114-torsion field degree: $2880$
Full 114-torsion field degree: $984960$

Jacobian

Conductor: $?$
Simple: yes
Squarefree: yes
Decomposition: $1$
Newforms: not computed

Rational points

This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank Kernel decomposition
6.18.0.d.1 $6$ $2$ $2$ $0$ $0$ full Jacobian
114.12.1.k.1 $114$ $3$ $3$ $1$ $?$ dimension zero
114.18.0.a.1 $114$ $2$ $2$ $0$ $?$ full Jacobian
114.18.1.b.1 $114$ $2$ $2$ $1$ $?$ dimension zero

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

Covering curve Level Index Degree Genus Rank Kernel decomposition
228.72.3.gj.1 $228$ $2$ $2$ $3$ $?$ not computed
228.72.3.gn.1 $228$ $2$ $2$ $3$ $?$ not computed
228.72.3.le.1 $228$ $2$ $2$ $3$ $?$ not computed
228.72.3.lh.1 $228$ $2$ $2$ $3$ $?$ not computed
228.72.3.sg.1 $228$ $2$ $2$ $3$ $?$ not computed
228.72.3.sj.1 $228$ $2$ $2$ $3$ $?$ not computed
228.72.3.tl.1 $228$ $2$ $2$ $3$ $?$ not computed
228.72.3.tp.1 $228$ $2$ $2$ $3$ $?$ not computed