Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2240.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2240.u1 2240w3 \([0, 1, 0, -525, 4673]\) \(-250523582464/13671875\) \(-875000000\) \([]\) \(864\) \(0.47404\)  
2240.u2 2240w1 \([0, 1, 0, -5, -7]\) \(-262144/35\) \(-2240\) \([]\) \(96\) \(-0.62458\) \(\Gamma_0(N)\)-optimal
2240.u3 2240w2 \([0, 1, 0, 35, 25]\) \(71991296/42875\) \(-2744000\) \([]\) \(288\) \(-0.075270\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2240.2.a.u

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