Properties

Label 1290.e
Number of curves $4$
Conductor $1290$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1290.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1290.e1 1290d3 [1, 0, 1, -839, 9212] [2] 768  
1290.e2 1290d2 [1, 0, 1, -89, -88] [2, 2] 384  
1290.e3 1290d1 [1, 0, 1, -69, -224] [2] 192 \(\Gamma_0(N)\)-optimal
1290.e4 1290d4 [1, 0, 1, 341, -604] [2] 768  

Rank

sage: E.rank()
 

The elliptic curves in class 1290.e have rank \(0\).

Complex multiplication

The elliptic curves in class 1290.e do not have complex multiplication.

Modular form 1290.2.a.e

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + 4q^{7} - q^{8} + q^{9} + q^{10} + q^{12} - 2q^{13} - 4q^{14} - q^{15} + q^{16} + 2q^{17} - q^{18} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.