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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 8470.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8470.f1 | 8470o2 | \([1, 0, 1, -3028, -64374]\) | \(-209611155721/13720\) | \(-200874520\) | \([]\) | \(6480\) | \(0.64979\) | |
8470.f2 | 8470o1 | \([1, 0, 1, -3, -244]\) | \(-121/1750\) | \(-25621750\) | \([3]\) | \(2160\) | \(0.10048\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8470.f have rank \(0\).
Complex multiplication
The elliptic curves in class 8470.f do not have complex multiplication.Modular form 8470.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.