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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 116886.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116886.u1 | 116886j2 | \([1, 0, 1, -3688772954056, 2726910926533633046]\) | \(-3133382230165522315000208250857964625/153574604080128\) | \(-272066779178795639808\) | \([]\) | \(1077753600\) | \(5.3134\) | |
116886.u2 | 116886j1 | \([1, 0, 1, -45540006856, 3740684175189014]\) | \(-5895856113332931416918127084625/215771481613620039647232\) | \(-382252341738906331057489969152\) | \([]\) | \(359251200\) | \(4.7641\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 116886.u have rank \(1\).
Complex multiplication
The elliptic curves in class 116886.u do not have complex multiplication.Modular form 116886.2.a.u
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.