Properties

Label 2550b
Number of curves 6
Conductor 2550
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("2550.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2550b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2550.c5 2550b1 [1, 1, 0, -850, 8500] [2] 2048 \(\Gamma_0(N)\)-optimal
2550.c4 2550b2 [1, 1, 0, -2850, -49500] [2, 2] 4096  
2550.c2 2550b3 [1, 1, 0, -43350, -3492000] [2, 2] 8192  
2550.c6 2550b4 [1, 1, 0, 5650, -279000] [2] 8192  
2550.c1 2550b5 [1, 1, 0, -693600, -222626250] [2] 16384  
2550.c3 2550b6 [1, 1, 0, -41100, -3867750] [2] 16384  

Rank

sage: E.rank()
 

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

Modular form 2550.2.a.c

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

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.