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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 450072.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
450072.r1 | 450072r1 | \([0, 0, 0, -759, -3670]\) | \(259108432/118769\) | \(22165145856\) | \([2]\) | \(236544\) | \(0.68001\) | \(\Gamma_0(N)\)-optimal |
450072.r2 | 450072r2 | \([0, 0, 0, 2661, -27610]\) | \(2791456412/2056579\) | \(-1535227997184\) | \([2]\) | \(473088\) | \(1.0266\) |
Rank
sage: E.rank()
The elliptic curves in class 450072.r have rank \(0\).
Complex multiplication
The elliptic curves in class 450072.r do not have complex multiplication.Modular form 450072.2.a.r
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.