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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 84966.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
84966.k1 | 84966z2 | \([1, 1, 0, -3936041, 2974307589]\) | \(814544990575471/9268826496\) | \(76738340110006280832\) | \([2]\) | \(4644864\) | \(2.6289\) | |
84966.k2 | 84966z1 | \([1, 1, 0, -51881, 117896325]\) | \(-1865409391/724451328\) | \(-5997867413442379776\) | \([2]\) | \(2322432\) | \(2.2823\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 84966.k have rank \(0\).
Complex multiplication
The elliptic curves in class 84966.k do not have complex multiplication.Modular form 84966.2.a.k
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.