Properties

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

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

Elliptic curves in class 6240.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6240.e1 6240c2 \([0, -1, 0, -696, -6840]\) \(72929847752/5265\) \(2695680\) \([2]\) \(2048\) \(0.28534\)  
6240.e2 6240c3 \([0, -1, 0, -241, 1441]\) \(379503424/24375\) \(99840000\) \([2]\) \(2048\) \(0.28534\)  
6240.e3 6240c1 \([0, -1, 0, -46, -80]\) \(171879616/38025\) \(2433600\) \([2, 2]\) \(1024\) \(-0.061236\) \(\Gamma_0(N)\)-optimal
6240.e4 6240c4 \([0, -1, 0, 104, -620]\) \(240641848/428415\) \(-219348480\) \([2]\) \(2048\) \(0.28534\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 6240.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} + 4 q^{11} + q^{13} + q^{15} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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 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.