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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 41382.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41382.bg1 | 41382c2 | \([1, -1, 0, -202758, 35249858]\) | \(-26436959739/50578\) | \(-1763636407274214\) | \([]\) | \(518400\) | \(1.8150\) | |
41382.bg2 | 41382c1 | \([1, -1, 0, 4152, 236088]\) | \(165469149/603592\) | \(-28871101272024\) | \([]\) | \(172800\) | \(1.2657\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 41382.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 41382.bg do not have complex multiplication.Modular form 41382.2.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.