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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 129285ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 129285.ba2 | 129285ba1 | \([0, 0, 1, -8112, 488790]\) | \(-2835349504/3316275\) | \(-69048058970475\) | \([]\) | \(262656\) | \(1.3495\) | \(\Gamma_0(N)\)-optimal |
| 129285.ba1 | 129285ba2 | \([0, 0, 1, -783822, 267100317]\) | \(-2557850287243264/796875\) | \(-16591709671875\) | \([3]\) | \(787968\) | \(1.8988\) |
Rank
sage: E.rank()
The elliptic curves in class 129285ba have rank \(1\).
Complex multiplication
The elliptic curves in class 129285ba do not have complex multiplication.Modular form 129285.2.a.ba
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.
