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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 110976.bf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
110976.bf1 | 110976n1 | \([0, 1, 0, -963, 9141]\) | \(16000/3\) | \(18537652992\) | \([2]\) | \(73728\) | \(0.68816\) | \(\Gamma_0(N)\)-optimal |
110976.bf2 | 110976n2 | \([0, 1, 0, 1927, 55959]\) | \(4000/9\) | \(-1779614687232\) | \([2]\) | \(147456\) | \(1.0347\) |
Rank
sage: E.rank()
The elliptic curves in class 110976.bf have rank \(0\).
Complex multiplication
The elliptic curves in class 110976.bf do not have complex multiplication.Modular form 110976.2.a.bf
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.