Properties

Label 47040hh
Number of curves $4$
Conductor $47040$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("hh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 47040hh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47040.fx3 47040hh1 \([0, 1, 0, -1780, 13838]\) \(82881856/36015\) \(271176239040\) \([2]\) \(73728\) \(0.88997\) \(\Gamma_0(N)\)-optimal
47040.fx2 47040hh2 \([0, 1, 0, -13785, -617625]\) \(601211584/11025\) \(5312840601600\) \([2, 2]\) \(147456\) \(1.2365\)  
47040.fx4 47040hh3 \([0, 1, 0, -65, -1778337]\) \(-8/354375\) \(-1366159011840000\) \([4]\) \(294912\) \(1.5831\)  
47040.fx1 47040hh4 \([0, 1, 0, -219585, -39678465]\) \(303735479048/105\) \(404787855360\) \([2]\) \(294912\) \(1.5831\)  

Rank

sage: E.rank()
 

The elliptic curves in class 47040hh have rank \(1\).

Complex multiplication

The elliptic curves in class 47040hh do not have complex multiplication.

Modular form 47040.2.a.hh

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{9} - 4q^{11} + 6q^{13} + q^{15} + 6q^{17} + 4q^{19} + O(q^{20})\)  Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.