Properties

Label 6240.l
Number of curves $2$
Conductor $6240$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6240.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6240.l1 6240g2 \([0, -1, 0, -40, 40]\) \(14172488/7605\) \(3893760\) \([2]\) \(768\) \(-0.044240\)  
6240.l2 6240g1 \([0, -1, 0, 10, 0]\) \(1560896/975\) \(-62400\) \([2]\) \(384\) \(-0.39081\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 6240.2.a.l

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