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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 10944.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10944.bc1 | 10944cj1 | \([0, 0, 0, -55020, -4966576]\) | \(96386901625/18468\) | \(3529289760768\) | \([2]\) | \(30720\) | \(1.4083\) | \(\Gamma_0(N)\)-optimal |
10944.bc2 | 10944cj2 | \([0, 0, 0, -49260, -6047152]\) | \(-69173457625/42633378\) | \(-8147365412732928\) | \([2]\) | \(61440\) | \(1.7549\) |
Rank
sage: E.rank()
The elliptic curves in class 10944.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 10944.bc do not have complex multiplication.Modular form 10944.2.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.