Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3920.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3920.w1 3920be1 \([0, 1, 0, -48820, 4138168]\) \(-177953104/125\) \(-9039207968000\) \([]\) \(12096\) \(1.4223\) \(\Gamma_0(N)\)-optimal
3920.w2 3920be2 \([0, 1, 0, 47220, 17660600]\) \(161017136/1953125\) \(-141237624500000000\) \([]\) \(36288\) \(1.9716\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3920.2.a.w

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