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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 397488.bp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
397488.bp1 | 397488bp2 | \([0, -1, 0, -367124, 79442700]\) | \(109744/9\) | \(448771169548945152\) | \([2]\) | \(5806080\) | \(2.1297\) | |
397488.bp2 | 397488bp1 | \([0, -1, 0, -77289, -6812196]\) | \(16384/3\) | \(9349399365603024\) | \([2]\) | \(2903040\) | \(1.7831\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 397488.bp have rank \(1\).
Complex multiplication
The elliptic curves in class 397488.bp do not have complex multiplication.Modular form 397488.2.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.