↑

Properties

Label 2550.x
Number of curves $2$
Conductor $2550$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 2550.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2550.x1 2550r2 \([1, 1, 1, -58239553, -171080620609]\) \(873851835888094527083289145/83719665273003835392\) \(2092991631825095884800\) \([]\) \(257040\) \(3.1276\)  
2550.x2 2550r1 \([1, 1, 1, -1541578, 390414551]\) \(16206164115169540524745/6736014906011025408\) \(168400372650275635200\) \([]\) \(85680\) \(2.5783\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2550.2.a.x

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.