Properties

Label 154560.cw
Number of curves $2$
Conductor $154560$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cw1")
 
E.isogeny_class()
 

Elliptic curves in class 154560.cw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
154560.cw1 154560da1 \([0, -1, 0, -40405, -3112475]\) \(7124261256822784/475453125\) \(486864000000\) \([2]\) \(552960\) \(1.2982\) \(\Gamma_0(N)\)-optimal
154560.cw2 154560da2 \([0, -1, 0, -37905, -3516975]\) \(-367624742361424/115740505125\) \(-1896292435968000\) \([2]\) \(1105920\) \(1.6448\)  

Rank

sage: E.rank()
 

The elliptic curves in class 154560.cw have rank \(0\).

Complex multiplication

The elliptic curves in class 154560.cw do not have complex multiplication.

Modular form 154560.2.a.cw

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - q^{7} + q^{9} + 4 q^{11} - 6 q^{13} - q^{15} - 6 q^{17} + 6 q^{19} + O(q^{20})\) 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.