Properties

Label 3920d
Number of curves 4
Conductor 3920
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("3920.s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3920d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3920.s3 3920d1 [0, 0, 0, -98, 343] [2] 576 \(\Gamma_0(N)\)-optimal
3920.s2 3920d2 [0, 0, 0, -343, -2058] [2, 2] 1152  
3920.s1 3920d3 [0, 0, 0, -5243, -146118] [2] 2304  
3920.s4 3920d4 [0, 0, 0, 637, -11662] [2] 2304  

Rank

sage: E.rank()
 

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

Modular form 3920.2.a.s

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

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.