Properties

Label 490.e
Number of curves $2$
Conductor $490$
CM no
Rank $0$
Graph

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

Elliptic curves in class 490.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
490.e1 490k1 \([1, -1, 1, -132, -549]\) \(-5154200289/20\) \(-980\) \([]\) \(120\) \(-0.21282\) \(\Gamma_0(N)\)-optimal
490.e2 490k2 \([1, -1, 1, 918, 5289]\) \(1747829720511/1280000000\) \(-62720000000\) \([7]\) \(840\) \(0.76013\)  

Rank

sage: E.rank()
 

The elliptic curves in class 490.e have rank \(0\).

Complex multiplication

The elliptic curves in class 490.e do not have complex multiplication.

Modular form 490.2.a.e

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.