Properties

Label 3600.be
Number of curves 4
Conductor 3600
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("3600.be1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3600.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3600.be1 3600bh3 [0, 0, 0, -9300, -345125] [2] 3456  
3600.be2 3600bh4 [0, 0, 0, -8175, -431750] [2] 6912  
3600.be3 3600bh1 [0, 0, 0, -300, 1375] [2] 1152 \(\Gamma_0(N)\)-optimal
3600.be4 3600bh2 [0, 0, 0, 825, 9250] [2] 2304  

Rank

sage: E.rank()
 

The elliptic curves in class 3600.be have rank \(1\).

Modular form 3600.2.a.be

sage: E.q_eigenform(10)
 
\( q + 2q^{7} - 2q^{13} - 6q^{17} + 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.