Properties

Label 6240.x
Number of curves $4$
Conductor $6240$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6240.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6240.x1 6240k2 \([0, 1, 0, -1256, -17556]\) \(428320044872/73125\) \(37440000\) \([2]\) \(3072\) \(0.45975\)  
6240.x2 6240k3 \([0, 1, 0, -536, 4440]\) \(33324076232/1285245\) \(658045440\) \([2]\) \(3072\) \(0.45975\)  
6240.x3 6240k1 \([0, 1, 0, -86, -240]\) \(1111934656/342225\) \(21902400\) \([2, 2]\) \(1536\) \(0.11317\) \(\Gamma_0(N)\)-optimal
6240.x4 6240k4 \([0, 1, 0, 239, -1345]\) \(367061696/426465\) \(-1746800640\) \([2]\) \(3072\) \(0.45975\)  

Rank

sage: E.rank()
 

The elliptic curves in class 6240.x have rank \(0\).

Complex multiplication

The elliptic curves in class 6240.x do not have complex multiplication.

Modular form 6240.2.a.x

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + 4q^{7} + q^{9} + 4q^{11} - q^{13} - q^{15} + 2q^{17} - 4q^{19} + O(q^{20})\)  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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.