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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 433200.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
433200.bc1 | 433200bc2 | \([0, -1, 0, -109458208, 440805034912]\) | \(112363774/3\) | \(3872252373348000000000\) | \([2]\) | \(58368000\) | \(3.2473\) | \(\Gamma_0(N)\)-optimal* |
433200.bc2 | 433200bc1 | \([0, -1, 0, -6573208, 7453414912]\) | \(-48668/9\) | \(-5808378560022000000000\) | \([2]\) | \(29184000\) | \(2.9007\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 433200.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 433200.bc do not have complex multiplication.Modular form 433200.2.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.