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Properties

Label 2550.b
Number of curves $4$
Conductor $2550$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 2550.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2550.b1 2550d4 \([1, 1, 0, -1310125, -577734125]\) \(15916310615119911121/2210850\) \(34544531250\) \([2]\) \(20736\) \(1.8763\)  
2550.b2 2550d3 \([1, 1, 0, -81875, -9054375]\) \(-3884775383991601/1448254140\) \(-22628970937500\) \([2]\) \(10368\) \(1.5297\)  
2550.b3 2550d2 \([1, 1, 0, -16375, -777875]\) \(31080575499121/1549125000\) \(24205078125000\) \([2]\) \(6912\) \(1.3270\)  
2550.b4 2550d1 \([1, 1, 0, 625, -46875]\) \(1723683599/62424000\) \(-975375000000\) \([2]\) \(3456\) \(0.98042\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2550.b have rank \(0\).

Complex multiplication

The elliptic curves in class 2550.b do not have complex multiplication.

Modular form 2550.2.a.b

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.