Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("3920.t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3920ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3920.t4 3920ba1 [0, 0, 0, 1813, -47334] [2] 4608 \(\Gamma_0(N)\)-optimal
3920.t3 3920ba2 [0, 0, 0, -13867, -508326] [2, 2] 9216  
3920.t1 3920ba3 [0, 0, 0, -209867, -37003526] [2] 18432  
3920.t2 3920ba4 [0, 0, 0, -68747, 6483386] [4] 18432  

Rank

sage: E.rank()
 

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

Modular form 3920.2.a.t

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

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.