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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 272734.bp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
272734.bp1 | 272734bp2 | \([1, 1, 0, -1031769, 402460997]\) | \(582810602977/829472\) | \(172880528457183008\) | \([2]\) | \(5376000\) | \(2.2106\) | |
272734.bp2 | 272734bp1 | \([1, 1, 0, -83129, 2324645]\) | \(304821217/164864\) | \(34361347270992896\) | \([2]\) | \(2688000\) | \(1.8640\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 272734.bp have rank \(0\).
Complex multiplication
The elliptic curves in class 272734.bp do not have complex multiplication.Modular form 272734.2.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 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.