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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 308550.bp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
308550.bp1 | 308550bp1 | \([1, 1, 0, -25723150, -50225168000]\) | \(68001744211490809/1022422500\) | \(28301309789414062500\) | \([2]\) | \(23224320\) | \(2.8690\) | \(\Gamma_0(N)\)-optimal |
308550.bp2 | 308550bp2 | \([1, 1, 0, -24966900, -53315961750]\) | \(-62178675647294809/8362782148050\) | \(-231487167265337594531250\) | \([2]\) | \(46448640\) | \(3.2156\) |
Rank
sage: E.rank()
The elliptic curves in class 308550.bp have rank \(1\).
Complex multiplication
The elliptic curves in class 308550.bp do not have complex multiplication.Modular form 308550.2.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.