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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 106722.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
106722.f1 | 106722cj2 | \([1, -1, 0, -112557693474, -11790893107312236]\) | \(779828911477214942771/154308452600236032\) | \(31206111149180758352193804375447552\) | \([2]\) | \(1570111488\) | \(5.3352\) | |
106722.f2 | 106722cj1 | \([1, -1, 0, -106547110434, -13385639031234156]\) | \(661452718394879874611/36407410163712\) | \(7362744354426065047706016940032\) | \([2]\) | \(785055744\) | \(4.9887\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 106722.f have rank \(1\).
Complex multiplication
The elliptic curves in class 106722.f do not have complex multiplication.Modular form 106722.2.a.f
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.