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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 450840.cc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
450840.cc1 | 450840cc2 | \([0, 1, 0, -622483316, -5977984190880]\) | \(21208997008348807455199568/61790625\) | \(77715799200000\) | \([2]\) | \(60456960\) | \(3.2620\) | \(\Gamma_0(N)\)-optimal* |
450840.cc2 | 450840cc1 | \([0, 1, 0, -38905191, -93415809630]\) | \(-82847542748407455193088/141410419921875\) | \(-11115990289218750000\) | \([2]\) | \(30228480\) | \(2.9155\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 450840.cc have rank \(0\).
Complex multiplication
The elliptic curves in class 450840.cc do not have complex multiplication.Modular form 450840.2.a.cc
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.