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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 230384.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
230384.bg1 | 230384bg2 | \([0, -1, 0, -65864, 6551536]\) | \(-526919079577/2201024\) | \(-131994388004864\) | \([]\) | \(787968\) | \(1.5645\) | |
230384.bg2 | 230384bg1 | \([0, -1, 0, 1896, 46576]\) | \(12562583/23324\) | \(-1398729457664\) | \([]\) | \(262656\) | \(1.0152\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 230384.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 230384.bg do not have complex multiplication.Modular form 230384.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.