Properties

Label 1290f
Number of curves $2$
Conductor $1290$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1290f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1290.g2 1290f1 \([1, 0, 1, -38, 56]\) \(5841725401/1857600\) \(1857600\) \([2]\) \(288\) \(-0.093268\) \(\Gamma_0(N)\)-optimal
1290.g1 1290f2 \([1, 0, 1, -238, -1384]\) \(1481933914201/53916840\) \(53916840\) \([2]\) \(576\) \(0.25331\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1290f have rank \(1\).

Complex multiplication

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

Modular form 1290.2.a.f

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