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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 4400.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4400.bc1 | 4400bc2 | \([0, -1, 0, -9208, 396912]\) | \(-53969305/10648\) | \(-17036800000000\) | \([]\) | \(12960\) | \(1.2619\) | |
4400.bc2 | 4400bc1 | \([0, -1, 0, 792, -3088]\) | \(34295/22\) | \(-35200000000\) | \([]\) | \(4320\) | \(0.71264\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4400.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 4400.bc do not have complex multiplication.Modular form 4400.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.