Properties

Label 3920.bg
Number of curves $2$
Conductor $3920$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3920.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3920.bg1 3920w2 \([0, -1, 0, -19056, -1006144]\) \(544737993463/20000\) \(28098560000\) \([2]\) \(7680\) \(1.0925\)  
3920.bg2 3920w1 \([0, -1, 0, -1136, -16960]\) \(-115501303/25600\) \(-35966156800\) \([2]\) \(3840\) \(0.74595\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3920.bg have rank \(1\).

Complex multiplication

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

Modular form 3920.2.a.bg

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.