Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3920.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3920.j1 3920bh2 \([0, 1, 0, -933760, 346974900]\) \(544737993463/20000\) \(3305767485440000\) \([2]\) \(53760\) \(2.0655\)  
3920.j2 3920bh1 \([0, 1, 0, -55680, 5928628]\) \(-115501303/25600\) \(-4231382381363200\) \([2]\) \(26880\) \(1.7189\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3920.2.a.j

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.