Properties

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

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 6240v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6240.b2 6240v1 \([0, -1, 0, -1966, 41080]\) \(-13137573612736/3427734375\) \(-219375000000\) \([2]\) \(5760\) \(0.89314\) \(\Gamma_0(N)\)-optimal
6240.b1 6240v2 \([0, -1, 0, -33216, 2341080]\) \(7916055336451592/385003125\) \(197121600000\) \([2]\) \(11520\) \(1.2397\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 6240.2.a.v

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - 2 q^{7} + q^{9} - q^{13} + q^{15} + 6 q^{19} + O(q^{20})\) 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.