Properties

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

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

Elliptic curves in class 2240.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2240.q1 2240y4 \([0, 0, 0, -17132, 863056]\) \(2121328796049/120050\) \(31470387200\) \([4]\) \(3072\) \(1.0787\)  
2240.q2 2240y3 \([0, 0, 0, -5612, -151216]\) \(74565301329/5468750\) \(1433600000000\) \([2]\) \(3072\) \(1.0787\)  
2240.q3 2240y2 \([0, 0, 0, -1132, 11856]\) \(611960049/122500\) \(32112640000\) \([2, 2]\) \(1536\) \(0.73213\)  
2240.q4 2240y1 \([0, 0, 0, 148, 1104]\) \(1367631/2800\) \(-734003200\) \([2]\) \(768\) \(0.38556\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 2240.q do not have complex multiplication.

Modular form 2240.2.a.q

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