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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 273273.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
273273.s1 | 273273s2 | \([1, 0, 0, -29484673, -38067195622]\) | \(14553591673375/5208653241\) | \(1014537068896906976604183\) | \([2]\) | \(38707200\) | \(3.3072\) | |
273273.s2 | 273273s1 | \([1, 0, 0, 5585362, -4182527805]\) | \(98931640625/96059601\) | \(-18710407763530825204863\) | \([2]\) | \(19353600\) | \(2.9607\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 273273.s have rank \(0\).
Complex multiplication
The elliptic curves in class 273273.s do not have complex multiplication.Modular form 273273.2.a.s
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.