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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 202160.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
202160.bg1 | 202160bg2 | \([0, 0, 0, -6094763, 5912478938]\) | \(-46905074216911089/1146880000000\) | \(-612198598574080000000\) | \([]\) | \(7112448\) | \(2.7739\) | |
202160.bg2 | 202160bg1 | \([0, 0, 0, -29963, -6684998]\) | \(-5573207889/32941720\) | \(-17584119366123520\) | \([]\) | \(1016064\) | \(1.8009\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 202160.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 202160.bg do not have complex multiplication.Modular form 202160.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.