Properties

Label 3640.e
Number of curves $4$
Conductor $3640$
CM no
Rank $0$
Graph

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

Elliptic curves in class 3640.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3640.e1 3640c3 \([0, 0, 0, -1403, -20218]\) \(298261205316/156065\) \(159810560\) \([2]\) \(1536\) \(0.52463\)  
3640.e2 3640c4 \([0, 0, 0, -803, 8622]\) \(55920415716/999635\) \(1023626240\) \([2]\) \(1536\) \(0.52463\)  
3640.e3 3640c2 \([0, 0, 0, -103, -198]\) \(472058064/207025\) \(52998400\) \([2, 2]\) \(768\) \(0.17806\)  
3640.e4 3640c1 \([0, 0, 0, 22, -23]\) \(73598976/56875\) \(-910000\) \([2]\) \(384\) \(-0.16852\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3640.e have rank \(0\).

Complex multiplication

The elliptic curves in class 3640.e do not have complex multiplication.

Modular form 3640.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{5} + q^{7} - 3 q^{9} - q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.