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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 86640bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 86640.u2 | 86640bp1 | \([0, -1, 0, -36581, -2647320]\) | \(1048576/15\) | \(77445047466960\) | \([2]\) | \(364800\) | \(1.4694\) | \(\Gamma_0(N)\)-optimal |
| 86640.u1 | 86640bp2 | \([0, -1, 0, -70876, 3141676]\) | \(476656/225\) | \(18586811392070400\) | \([2]\) | \(729600\) | \(1.8159\) |
Rank
sage: E.rank()
The elliptic curves in class 86640bp have rank \(0\).
Complex multiplication
The elliptic curves in class 86640bp do not have complex multiplication.Modular form 86640.2.a.bp
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.
