Properties

Label 2240.k
Number of curves $3$
Conductor $2240$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2240.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2240.k1 2240m3 \([0, -1, 0, -525, -4673]\) \(-250523582464/13671875\) \(-875000000\) \([]\) \(864\) \(0.47404\)  
2240.k2 2240m1 \([0, -1, 0, -5, 7]\) \(-262144/35\) \(-2240\) \([]\) \(96\) \(-0.62458\) \(\Gamma_0(N)\)-optimal
2240.k3 2240m2 \([0, -1, 0, 35, -25]\) \(71991296/42875\) \(-2744000\) \([]\) \(288\) \(-0.075270\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2240.k have rank \(1\).

Complex multiplication

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

Modular form 2240.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{7} - 2 q^{9} + 3 q^{11} - 5 q^{13} - q^{15} + 3 q^{17} - 2 q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.