Properties

Label 2240.q
Number of curves $4$
Conductor $2240$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("2240.q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2240.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2240.q1 2240y4 [0, 0, 0, -17132, 863056] [4] 3072  
2240.q2 2240y3 [0, 0, 0, -5612, -151216] [2] 3072  
2240.q3 2240y2 [0, 0, 0, -1132, 11856] [2, 2] 1536  
2240.q4 2240y1 [0, 0, 0, 148, 1104] [2] 768 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2240.q have rank \(0\).

Modular form 2240.2.a.q

sage: E.q_eigenform(10)
 
\( q + q^{5} + q^{7} - 3q^{9} + 4q^{11} + 6q^{13} + 2q^{17} + O(q^{20}) \)

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.