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SageMath
E = EllipticCurve("kw1")
E.isogeny_class()
Elliptic curves in class 100800kw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100800.id2 | 100800kw1 | \([0, 0, 0, -19500, 450000]\) | \(59319/28\) | \(387072000000000\) | \([2]\) | \(368640\) | \(1.4933\) | \(\Gamma_0(N)\)-optimal |
100800.id1 | 100800kw2 | \([0, 0, 0, -259500, 50850000]\) | \(139798359/98\) | \(1354752000000000\) | \([2]\) | \(737280\) | \(1.8399\) |
Rank
sage: E.rank()
The elliptic curves in class 100800kw have rank \(0\).
Complex multiplication
The elliptic curves in class 100800kw do not have complex multiplication.Modular form 100800.2.a.kw
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 Cremona 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 Cremona labels.