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Properties

Label 312.48.1.baa.1
Level $312$
Index $48$
Genus $1$
Cusps $8$
$\Q$-cusps $4$

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Invariants

Level: $312$ $\SL_2$-level: $24$ Newform level: $1$
Index: $48$ $\PSL_2$-index:$48$
Genus: $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$
Cusps: $8$ (of which $4$ are rational) Cusp widths $1^{2}\cdot2\cdot3^{2}\cdot6\cdot8\cdot24$ Cusp orbits $1^{4}\cdot2^{2}$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: not computed
$\Q$-gonality: $2$
$\overline{\Q}$-gonality: $2$
Rational cusps: $4$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 24G1

Level structure

$\GL_2(\Z/312\Z)$-generators: $\begin{bmatrix}86&103\\131&90\end{bmatrix}$, $\begin{bmatrix}115&170\\42&299\end{bmatrix}$, $\begin{bmatrix}119&34\\192&133\end{bmatrix}$, $\begin{bmatrix}210&41\\107&156\end{bmatrix}$, $\begin{bmatrix}270&109\\203&304\end{bmatrix}$, $\begin{bmatrix}293&180\\246&119\end{bmatrix}$, $\begin{bmatrix}294&1\\5&178\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 312.96.1-312.baa.1.1, 312.96.1-312.baa.1.2, 312.96.1-312.baa.1.3, 312.96.1-312.baa.1.4, 312.96.1-312.baa.1.5, 312.96.1-312.baa.1.6, 312.96.1-312.baa.1.7, 312.96.1-312.baa.1.8, 312.96.1-312.baa.1.9, 312.96.1-312.baa.1.10, 312.96.1-312.baa.1.11, 312.96.1-312.baa.1.12, 312.96.1-312.baa.1.13, 312.96.1-312.baa.1.14, 312.96.1-312.baa.1.15, 312.96.1-312.baa.1.16, 312.96.1-312.baa.1.17, 312.96.1-312.baa.1.18, 312.96.1-312.baa.1.19, 312.96.1-312.baa.1.20, 312.96.1-312.baa.1.21, 312.96.1-312.baa.1.22, 312.96.1-312.baa.1.23, 312.96.1-312.baa.1.24, 312.96.1-312.baa.1.25, 312.96.1-312.baa.1.26, 312.96.1-312.baa.1.27, 312.96.1-312.baa.1.28, 312.96.1-312.baa.1.29, 312.96.1-312.baa.1.30, 312.96.1-312.baa.1.31, 312.96.1-312.baa.1.32, 312.96.1-312.baa.1.33, 312.96.1-312.baa.1.34, 312.96.1-312.baa.1.35, 312.96.1-312.baa.1.36, 312.96.1-312.baa.1.37, 312.96.1-312.baa.1.38, 312.96.1-312.baa.1.39, 312.96.1-312.baa.1.40, 312.96.1-312.baa.1.41, 312.96.1-312.baa.1.42, 312.96.1-312.baa.1.43, 312.96.1-312.baa.1.44, 312.96.1-312.baa.1.45, 312.96.1-312.baa.1.46, 312.96.1-312.baa.1.47, 312.96.1-312.baa.1.48, 312.96.1-312.baa.1.49, 312.96.1-312.baa.1.50, 312.96.1-312.baa.1.51, 312.96.1-312.baa.1.52, 312.96.1-312.baa.1.53, 312.96.1-312.baa.1.54, 312.96.1-312.baa.1.55, 312.96.1-312.baa.1.56, 312.96.1-312.baa.1.57, 312.96.1-312.baa.1.58, 312.96.1-312.baa.1.59, 312.96.1-312.baa.1.60, 312.96.1-312.baa.1.61, 312.96.1-312.baa.1.62, 312.96.1-312.baa.1.63, 312.96.1-312.baa.1.64
Cyclic 312-isogeny field degree: $28$
Cyclic 312-torsion field degree: $2688$
Full 312-torsion field degree: $40255488$

Jacobian

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

Rational points

This modular curve is an elliptic curve, but the rank has not been computed

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
$X_0(3)$ $3$ $12$ $12$ $0$ $0$ full Jacobian
104.12.0.ba.1 $104$ $4$ $4$ $0$ $?$ full Jacobian

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank Kernel decomposition
$X_0(12)$ $12$ $2$ $2$ $0$ $0$ full Jacobian
104.12.0.ba.1 $104$ $4$ $4$ $0$ $?$ full Jacobian

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

Covering curve Level Index Degree Genus Rank Kernel decomposition
312.96.1.rn.1 $312$ $2$ $2$ $1$ $?$ dimension zero
312.96.1.rn.2 $312$ $2$ $2$ $1$ $?$ dimension zero
312.96.1.rn.3 $312$ $2$ $2$ $1$ $?$ dimension zero
312.96.1.rn.4 $312$ $2$ $2$ $1$ $?$ dimension zero
312.96.1.rp.1 $312$ $2$ $2$ $1$ $?$ dimension zero
312.96.1.rp.2 $312$ $2$ $2$ $1$ $?$ dimension zero
312.96.1.rp.3 $312$ $2$ $2$ $1$ $?$ dimension zero
312.96.1.rp.4 $312$ $2$ $2$ $1$ $?$ dimension zero
312.96.1.sx.1 $312$ $2$ $2$ $1$ $?$ dimension zero
312.96.1.sx.2 $312$ $2$ $2$ $1$ $?$ dimension zero
312.96.1.sx.3 $312$ $2$ $2$ $1$ $?$ dimension zero
312.96.1.sx.4 $312$ $2$ $2$ $1$ $?$ dimension zero
312.96.1.sz.1 $312$ $2$ $2$ $1$ $?$ dimension zero
312.96.1.sz.2 $312$ $2$ $2$ $1$ $?$ dimension zero
312.96.1.sz.3 $312$ $2$ $2$ $1$ $?$ dimension zero
312.96.1.sz.4 $312$ $2$ $2$ $1$ $?$ dimension zero
312.96.3.gd.1 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.hq.1 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.ky.1 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.la.1 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.mc.1 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.me.1 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.mo.1 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.mq.1 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.nz.1 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.oa.1 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.pe.1 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.ph.1 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.pv.1 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.pw.1 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.qg.1 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.qj.1 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.su.1 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.su.2 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.su.3 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.su.4 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.sw.1 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.sw.2 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.sw.3 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.sw.4 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.ts.1 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.ts.2 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.ts.3 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.ts.4 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.tu.1 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.tu.2 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.tu.3 $312$ $2$ $2$ $3$ $?$ not computed
312.96.3.tu.4 $312$ $2$ $2$ $3$ $?$ not computed
312.144.5.po.1 $312$ $3$ $3$ $5$ $?$ not computed