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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)
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.