Properties

Label 1290.k
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 1290.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1290.k1 1290j2 \([1, 1, 1, -1336, 18239]\) \(263732349218689/4160250\) \(4160250\) \([2]\) \(576\) \(0.40401\)  
1290.k2 1290j1 \([1, 1, 1, -86, 239]\) \(70393838689/8062500\) \(8062500\) \([2]\) \(288\) \(0.057441\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1290.2.a.k

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.