Properties

Label 40560.cw
Number of curves $2$
Conductor $40560$
CM no
Rank $0$
Graph

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

Elliptic curves in class 40560.cw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40560.cw1 40560ct2 \([0, 1, 0, -124440, 15094548]\) \(10779215329/1232010\) \(24357588812144640\) \([2]\) \(387072\) \(1.8766\)  
40560.cw2 40560ct1 \([0, 1, 0, 10760, 1195988]\) \(6967871/35100\) \(-693948399206400\) \([2]\) \(193536\) \(1.5300\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 40560.cw have rank \(0\).

Complex multiplication

The elliptic curves in class 40560.cw do not have complex multiplication.

Modular form 40560.2.a.cw

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + 2 q^{7} + q^{9} + 4 q^{11} + q^{15} + 8 q^{17} - 6 q^{19} + O(q^{20})\) 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.