Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 2550.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2550.w1 2550u2 \([1, 1, 1, -663, -4179]\) \(1289333385625/482967552\) \(12074188800\) \([]\) \(2160\) \(0.63426\)  
2550.w2 2550u1 \([1, 1, 1, -288, 1761]\) \(105695235625/14688\) \(367200\) \([]\) \(720\) \(0.084957\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2550.2.a.w

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