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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 266560bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 266560.bp2 | 266560bp1 | \([0, -1, 0, 1251199, -167647199]\) | \(7023836099951/4456448000\) | \(-137441221214732288000\) | \([]\) | \(5806080\) | \(2.5531\) | \(\Gamma_0(N)\)-optimal |
| 266560.bp1 | 266560bp2 | \([0, -1, 0, -20826241, -37754288095]\) | \(-32391289681150609/1228250000000\) | \(-37880433016832000000000\) | \([]\) | \(17418240\) | \(3.1024\) |
Rank
sage: E.rank()
The elliptic curves in class 266560bp have rank \(0\).
Complex multiplication
The elliptic curves in class 266560bp do not have complex multiplication.Modular form 266560.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
