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Properties

Label 2550.s
Number of curves $2$
Conductor $2550$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 2550.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2550.s1 2550x2 \([1, 1, 1, -7253, 234731]\) \(337575153545189/2448\) \(306000\) \([2]\) \(2560\) \(0.64889\)  
2550.s2 2550x1 \([1, 1, 1, -453, 3531]\) \(-82256120549/221952\) \(-27744000\) \([2]\) \(1280\) \(0.30231\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2550.2.a.s

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.