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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 476850.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
476850.x1 | 476850x2 | \([1, 1, 0, -174060, -28023600]\) | \(949659180759757/46464\) | \(28534704000\) | \([2]\) | \(1720320\) | \(1.4821\) | \(\Gamma_0(N)\)-optimal* |
476850.x2 | 476850x1 | \([1, 1, 0, -10860, -442800]\) | \(-230684754637/1622016\) | \(-996120576000\) | \([2]\) | \(860160\) | \(1.1355\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 476850.x have rank \(1\).
Complex multiplication
The elliptic curves in class 476850.x do not have complex multiplication.Modular form 476850.2.a.x
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.