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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 966k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
966.i2 | 966k1 | \([1, 0, 0, 3, 9]\) | \(2924207/34776\) | \(-34776\) | \([3]\) | \(120\) | \(-0.44771\) | \(\Gamma_0(N)\)-optimal |
966.i1 | 966k2 | \([1, 0, 0, -27, -249]\) | \(-2181825073/25039686\) | \(-25039686\) | \([]\) | \(360\) | \(0.10160\) |
Rank
sage: E.rank()
The elliptic curves in class 966k have rank \(0\).
Complex multiplication
The elliptic curves in class 966k do not have complex multiplication.Modular form 966.2.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 Cremona 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 Cremona labels.