Properties

Label 5550.bd
Number of curves $4$
Conductor $5550$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5550.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5550.bd1 5550x4 \([1, 1, 1, -262188, -23175219]\) \(127568139540190201/59114336463360\) \(923661507240000000\) \([2]\) \(145152\) \(2.1419\)  
5550.bd2 5550x2 \([1, 1, 1, -132813, 18573531]\) \(16581570075765001/998001000\) \(15593765625000\) \([2]\) \(48384\) \(1.5926\)  
5550.bd3 5550x1 \([1, 1, 1, -7813, 323531]\) \(-3375675045001/999000000\) \(-15609375000000\) \([2]\) \(24192\) \(1.2460\) \(\Gamma_0(N)\)-optimal
5550.bd4 5550x3 \([1, 1, 1, 57812, -2695219]\) \(1367594037332999/995878502400\) \(-15560601600000000\) \([2]\) \(72576\) \(1.7953\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5550.bd have rank \(0\).

Complex multiplication

The elliptic curves in class 5550.bd do not have complex multiplication.

Modular form 5550.2.a.bd

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} + 4q^{7} + q^{8} + q^{9} + 6q^{11} - q^{12} - 2q^{13} + 4q^{14} + q^{16} + 6q^{17} + q^{18} + 2q^{19} + O(q^{20})\)  Toggle raw display

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.