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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 116886.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116886.j1 | 116886n2 | \([1, 0, 1, -1981983, -340077278]\) | \(486034459476995521/253095136942032\) | \(448373473896163151952\) | \([2]\) | \(6635520\) | \(2.6546\) | |
116886.j2 | 116886n1 | \([1, 0, 1, 467057, -41294398]\) | \(6360314548472639/4097346156288\) | \(-7258698653979725568\) | \([2]\) | \(3317760\) | \(2.3080\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 116886.j have rank \(1\).
Complex multiplication
The elliptic curves in class 116886.j do not have complex multiplication.Modular form 116886.2.a.j
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.