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SageMath
E = EllipticCurve("eo1")
E.isogeny_class()
Elliptic curves in class 350658.eo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
350658.eo1 | 350658eo2 | \([1, -1, 1, -17837843, 9182086499]\) | \(486034459476995521/253095136942032\) | \(326864262470302937773008\) | \([2]\) | \(53084160\) | \(3.2039\) | |
350658.eo2 | 350658eo1 | \([1, -1, 1, 4203517, 1114948739]\) | \(6360314548472639/4097346156288\) | \(-5291591318751219939072\) | \([2]\) | \(26542080\) | \(2.8573\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 350658.eo have rank \(1\).
Complex multiplication
The elliptic curves in class 350658.eo do not have complex multiplication.Modular form 350658.2.a.eo
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.