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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 129285s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 129285.e1 | 129285s1 | \([1, -1, 1, -21883673, 39408392872]\) | \(329379602649536529/690625\) | \(2430132409940625\) | \([2]\) | \(4300800\) | \(2.6283\) | \(\Gamma_0(N)\)-optimal |
| 129285.e2 | 129285s2 | \([1, -1, 1, -21876068, 39437145856]\) | \(-329036324603513409/476962890625\) | \(-1678310195615244140625\) | \([2]\) | \(8601600\) | \(2.9749\) |
Rank
sage: E.rank()
The elliptic curves in class 129285s have rank \(0\).
Complex multiplication
The elliptic curves in class 129285s do not have complex multiplication.Modular form 129285.2.a.s
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
