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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 1650.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1650.s1 | 1650s1 | \([1, 0, 0, -903, 10377]\) | \(-3257444411545/2737152\) | \(-68428800\) | \([5]\) | \(1200\) | \(0.43117\) | \(\Gamma_0(N)\)-optimal |
1650.s2 | 1650s2 | \([1, 0, 0, 6237, -87483]\) | \(2747555975/1932612\) | \(-18873164062500\) | \([]\) | \(6000\) | \(1.2359\) |
Rank
sage: E.rank()
The elliptic curves in class 1650.s have rank \(0\).
Complex multiplication
The elliptic curves in class 1650.s do not have complex multiplication.Modular form 1650.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.