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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 38025.cc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38025.cc1 | 38025bh1 | \([1, -1, 0, -38817, -616784]\) | \(117649/65\) | \(3573724132265625\) | \([2]\) | \(193536\) | \(1.6749\) | \(\Gamma_0(N)\)-optimal |
38025.cc2 | 38025bh2 | \([1, -1, 0, 151308, -4989659]\) | \(6967871/4225\) | \(-232292068597265625\) | \([2]\) | \(387072\) | \(2.0215\) |
Rank
sage: E.rank()
The elliptic curves in class 38025.cc have rank \(0\).
Complex multiplication
The elliptic curves in class 38025.cc do not have complex multiplication.Modular form 38025.2.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.