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SageMath
sage: E = EllipticCurve("h1")
sage: E.isogeny_class()
Elliptic curves in class 3528h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
3528.n2 | 3528h1 | [0, 0, 0, 5145, 369754] | [2] | 7168 | \(\Gamma_0(N)\)-optimal |
3528.n1 | 3528h2 | [0, 0, 0, -56595, 4605118] | [2] | 14336 |
Rank
sage: E.rank()
The elliptic curves in class 3528h have rank \(1\).
Complex multiplication
The elliptic curves in class 3528h do not have complex multiplication.Modular form 3528.2.a.h
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.