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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 2960.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2960.k1 | 2960g1 | \([0, -1, 0, -56, 176]\) | \(4826809/185\) | \(757760\) | \([2]\) | \(384\) | \(-0.10392\) | \(\Gamma_0(N)\)-optimal |
| 2960.k2 | 2960g2 | \([0, -1, 0, 24, 560]\) | \(357911/34225\) | \(-140185600\) | \([2]\) | \(768\) | \(0.24265\) |
Rank
sage: E.rank()
The elliptic curves in class 2960.k have rank \(0\).
Complex multiplication
The elliptic curves in class 2960.k do not have complex multiplication.Modular form 2960.2.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.
