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Properties

Label 650.g
Number of curves $2$
Conductor $650$
CM no
Rank $0$
Graph

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

Elliptic curves in class 650.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
650.g1 650f2 \([1, -1, 0, -5317, -162409]\) \(-1064019559329/125497034\) \(-1960891156250\) \([]\) \(1960\) \(1.0945\)  
650.g2 650f1 \([1, -1, 0, -67, 341]\) \(-2146689/1664\) \(-26000000\) \([]\) \(280\) \(0.12156\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 650.g have rank \(0\).

Complex multiplication

The elliptic curves in class 650.g do not have complex multiplication.

Modular form 650.2.a.g

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