Properties

Label 66240fe
Number of curves $2$
Conductor $66240$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("fe1")
 
E.isogeny_class()
 

Elliptic curves in class 66240fe

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
66240.h2 66240fe1 \([0, 0, 0, 95892, -5756848]\) \(510273943271/370215360\) \(-70749257056911360\) \([2]\) \(516096\) \(1.9215\) \(\Gamma_0(N)\)-optimal
66240.h1 66240fe2 \([0, 0, 0, -434028, -48786352]\) \(47316161414809/22001657400\) \(4204582206072422400\) \([2]\) \(1032192\) \(2.2681\)  

Rank

sage: E.rank()
 

The elliptic curves in class 66240fe have rank \(0\).

Complex multiplication

The elliptic curves in class 66240fe do not have complex multiplication.

Modular form 66240.2.a.fe

sage: E.q_eigenform(10)
 
\(q - q^{5} - 4 q^{7} + 2 q^{11} - 2 q^{17} + O(q^{20})\) 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.