Properties

Label 490.f
Number of curves $2$
Conductor $490$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("490.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 490.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
490.f1 490g2 [1, 0, 0, -1191, 15721] [2] 320  
490.f2 490g1 [1, 0, 0, -71, 265] [2] 160 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 490.f have rank \(1\).

Modular form 490.2.a.f

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.