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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 466578.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
466578.c1 | 466578c1 | \([1, -1, 0, -289438746, 1895394921748]\) | \(-5702623460245179/252448\) | \(-118710997624947452256\) | \([]\) | \(133816320\) | \(3.3340\) | \(\Gamma_0(N)\)-optimal |
466578.c2 | 466578c2 | \([1, -1, 0, -264943401, 2229373346381]\) | \(-5999796014211/2790817792\) | \(-956704973533149736447082496\) | \([]\) | \(401448960\) | \(3.8833\) |
Rank
sage: E.rank()
The elliptic curves in class 466578.c have rank \(1\).
Complex multiplication
The elliptic curves in class 466578.c do not have complex multiplication.Modular form 466578.2.a.c
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.