Properties

Label 4290.y
Number of curves $4$
Conductor $4290$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4290.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4290.y1 4290w3 \([1, 0, 0, -160426, -24744844]\) \(456612868287073618849/12544848030000\) \(12544848030000\) \([2]\) \(24576\) \(1.6167\)  
4290.y2 4290w4 \([1, 0, 0, -44746, 3289940]\) \(9908022260084596129/1047363281250000\) \(1047363281250000\) \([2]\) \(24576\) \(1.6167\)  
4290.y3 4290w2 \([1, 0, 0, -10426, -354844]\) \(125337052492018849/18404100000000\) \(18404100000000\) \([2, 2]\) \(12288\) \(1.2702\)  
4290.y4 4290w1 \([1, 0, 0, 1094, -29980]\) \(144794100308831/474439680000\) \(-474439680000\) \([4]\) \(6144\) \(0.92359\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4290.y have rank \(0\).

Complex multiplication

The elliptic curves in class 4290.y do not have complex multiplication.

Modular form 4290.2.a.y

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{8} + q^{9} - q^{10} - q^{11} + q^{12} + q^{13} - q^{15} + q^{16} + 6q^{17} + q^{18} + 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.