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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)
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.