Properties

Label 115600.dc
Number of curves 4
Conductor 115600
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("115600.dc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115600.dc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
115600.dc1 115600bz4 [0, -1, 0, -13065208, 12565212912] [2] 11943936  
115600.dc2 115600bz3 [0, -1, 0, -11909208, 15820508912] [2] 5971968  
115600.dc3 115600bz2 [0, -1, 0, -4973208, -4266147088] [2] 3981312  
115600.dc4 115600bz1 [0, -1, 0, -349208, -49059088] [2] 1990656 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 115600.dc have rank \(0\).

Modular form 115600.2.a.dc

sage: E.q_eigenform(10)
 
\( q + 2q^{3} + 4q^{7} + q^{9} + 6q^{11} - 2q^{13} + 4q^{19} + O(q^{20}) \)

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.