Properties

Label 2550.d
Number of curves $4$
Conductor $2550$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 2550.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2550.d1 2550a3 \([1, 1, 0, -4650, -123750]\) \(711882749089/1721250\) \(26894531250\) \([2]\) \(3072\) \(0.88009\)  
2550.d2 2550a4 \([1, 1, 0, -4150, 100750]\) \(506071034209/2505630\) \(39150468750\) \([2]\) \(3072\) \(0.88009\)  
2550.d3 2550a2 \([1, 1, 0, -400, -500]\) \(454756609/260100\) \(4064062500\) \([2, 2]\) \(1536\) \(0.53352\)  
2550.d4 2550a1 \([1, 1, 0, 100, 0]\) \(6967871/4080\) \(-63750000\) \([2]\) \(768\) \(0.18695\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2550.d have rank \(1\).

Complex multiplication

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

Modular form 2550.2.a.d

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.