Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 490.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
490.g1 490e2 \([1, 0, 0, -491, -4229]\) \(-5452947409/250\) \(-600250\) \([]\) \(180\) \(0.18439\)  
490.g2 490e1 \([1, 0, 0, -1, -15]\) \(-49/40\) \(-96040\) \([3]\) \(60\) \(-0.36492\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 490.2.a.g

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.