Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3920.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3920.k1 3920q1 \([0, -1, 0, -996, -11780]\) \(-177953104/125\) \(-76832000\) \([]\) \(1728\) \(0.44939\) \(\Gamma_0(N)\)-optimal
3920.k2 3920q2 \([0, -1, 0, 964, -51764]\) \(161017136/1953125\) \(-1200500000000\) \([]\) \(5184\) \(0.99869\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3920.2.a.k

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.