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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 485100.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
485100.bc1 | 485100bc2 | \([0, 0, 0, -46088175, 111454505750]\) | \(31558509702736/2620631475\) | \(899045584725033900000000\) | \([2]\) | \(63700992\) | \(3.3384\) | \(\Gamma_0(N)\)-optimal* |
485100.bc2 | 485100bc1 | \([0, 0, 0, 3028200, 7966303625]\) | \(143225913344/1361505915\) | \(-29192770262026428750000\) | \([2]\) | \(31850496\) | \(2.9919\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 485100.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 485100.bc do not have complex multiplication.Modular form 485100.2.a.bc
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.