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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 102960.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
102960.bc1 | 102960q2 | \([0, 0, 0, -2639883, -1650916582]\) | \(1362762798430761362/10456875\) | \(15612030720000\) | \([2]\) | \(917504\) | \(2.1243\) | |
102960.bc2 | 102960q1 | \([0, 0, 0, -164883, -25831582]\) | \(-664085303622724/1843359375\) | \(-1376060400000000\) | \([2]\) | \(458752\) | \(1.7777\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 102960.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 102960.bc do not have complex multiplication.Modular form 102960.2.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.