Properties

Label 3920.g
Number of curves $2$
Conductor $3920$
CM no
Rank $0$
Graph

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

Elliptic curves in class 3920.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3920.g1 3920bg2 \([0, 1, 0, -384960, -92065100]\) \(-5452947409/250\) \(-289254654976000\) \([]\) \(30240\) \(1.8505\)  
3920.g2 3920bg1 \([0, 1, 0, -800, -327692]\) \(-49/40\) \(-46280744796160\) \([]\) \(10080\) \(1.3012\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3920.g have rank \(0\).

Complex multiplication

The elliptic curves in class 3920.g do not have complex multiplication.

Modular form 3920.2.a.g

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