Properties

Label 1290k
Number of curves $2$
Conductor $1290$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1290k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1290.j2 1290k1 [1, 1, 1, -10256, -418831] [2] 5040 \(\Gamma_0(N)\)-optimal
1290.j1 1290k2 [1, 1, 1, -165776, -26048527] [2] 10080  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1290.2.a.k

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} - 4q^{7} + q^{8} + q^{9} - q^{10} - 4q^{11} - q^{12} + 4q^{13} - 4q^{14} + q^{15} + q^{16} + 4q^{17} + q^{18} + 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.