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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 397800.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 397800.k1 | 397800k2 | \([0, 0, 0, -2754675, -724079250]\) | \(3670232225814/1764381125\) | \(1111306037868000000000\) | \([2]\) | \(15482880\) | \(2.7321\) | |
| 397800.k2 | 397800k1 | \([0, 0, 0, 620325, -86204250]\) | \(83824368372/58703125\) | \(-18487257750000000000\) | \([2]\) | \(7741440\) | \(2.3855\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 397800.k have rank \(0\).
Complex multiplication
The elliptic curves in class 397800.k do not have complex multiplication.Modular form 397800.2.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.
