Properties

Label 5610.bc
Number of curves 6
Conductor 5610
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("5610.bc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5610.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5610.bc1 5610bb5 [1, 1, 1, -292140, -60890853] [2] 49152  
5610.bc2 5610bb3 [1, 1, 1, -19890, -778053] [2, 2] 24576  
5610.bc3 5610bb2 [1, 1, 1, -7390, 231947] [2, 4] 12288  
5610.bc4 5610bb1 [1, 1, 1, -7310, 237515] [4] 6144 \(\Gamma_0(N)\)-optimal
5610.bc5 5610bb4 [1, 1, 1, 3830, 887195] [4] 24576  
5610.bc6 5610bb6 [1, 1, 1, 52360, -5055253] [2] 49152  

Rank

sage: E.rank()
 

The elliptic curves in class 5610.bc have rank \(0\).

Modular form 5610.2.a.bc

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + q^{10} - q^{11} - q^{12} + 6q^{13} - q^{15} + q^{16} + q^{17} + q^{18} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.