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SageMath
E = EllipticCurve("gi1")
E.isogeny_class()
Elliptic curves in class 139650.gi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
139650.gi1 | 139650er2 | \([1, 1, 1, -2448188, 1470250781]\) | \(882774443450089/2166000000\) | \(3981683343750000000\) | \([2]\) | \(5806080\) | \(2.4472\) | |
139650.gi2 | 139650er1 | \([1, 1, 1, -96188, 40234781]\) | \(-53540005609/350208000\) | \(-643775328000000000\) | \([2]\) | \(2903040\) | \(2.1006\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 139650.gi have rank \(1\).
Complex multiplication
The elliptic curves in class 139650.gi do not have complex multiplication.Modular form 139650.2.a.gi
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.