Properties

Label 47610e
Number of curves $2$
Conductor $47610$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 47610e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47610.e2 47610e1 \([1, -1, 0, -33236640, 93568332800]\) \(-1015884369980369163/358196480000000\) \(-1431700227543709440000000\) \([2]\) \(9934848\) \(3.3461\) \(\Gamma_0(N)\)-optimal
47610.e1 47610e2 \([1, -1, 0, -570531360, 5245042649216]\) \(5138442430700033888523/413281250000000\) \(1651872345771093750000000\) \([2]\) \(19869696\) \(3.6927\)  

Rank

sage: E.rank()
 

The elliptic curves in class 47610e have rank \(0\).

Complex multiplication

The elliptic curves in class 47610e do not have complex multiplication.

Modular form 47610.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - 2 q^{7} - q^{8} + q^{10} + 6 q^{11} + 2 q^{14} + q^{16} - 2 q^{17} + 4 q^{19} + O(q^{20})\) Copy content 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.