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SageMath
E = EllipticCurve("dr1")
E.isogeny_class()
Elliptic curves in class 127296.dr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
127296.dr1 | 127296bf2 | \([0, 0, 0, -6749388, -6749082000]\) | \(177930109857804849/634933\) | \(121337585860608\) | \([2]\) | \(3932160\) | \(2.3442\) | |
127296.dr2 | 127296bf1 | \([0, 0, 0, -422028, -105354000]\) | \(43499078731809/82055753\) | \(15681098596220928\) | \([2]\) | \(1966080\) | \(1.9976\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 127296.dr have rank \(1\).
Complex multiplication
The elliptic curves in class 127296.dr do not have complex multiplication.Modular form 127296.2.a.dr
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.