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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 164730.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
164730.bg1 | 164730cd2 | \([1, 0, 1, -957319, 358402892]\) | \(818187429977/5343750\) | \(633703965030843750\) | \([2]\) | \(3133440\) | \(2.2517\) | |
164730.bg2 | 164730cd1 | \([1, 0, 1, -23849, 12272216]\) | \(-12649337/541500\) | \(-64215335123125500\) | \([2]\) | \(1566720\) | \(1.9052\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 164730.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 164730.bg do not have complex multiplication.Modular form 164730.2.a.bg
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.