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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 8016.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8016.f1 | 8016f2 | \([0, -1, 0, -1992, 34800]\) | \(213525509833/669336\) | \(2741600256\) | \([2]\) | \(6912\) | \(0.67830\) | |
8016.f2 | 8016f1 | \([0, -1, 0, -72, 1008]\) | \(-10218313/96192\) | \(-394002432\) | \([2]\) | \(3456\) | \(0.33172\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8016.f have rank \(0\).
Complex multiplication
The elliptic curves in class 8016.f do not have complex multiplication.Modular form 8016.2.a.f
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.