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SageMath
sage: E = EllipticCurve("858.k1")
sage: E.isogeny_class()
Elliptic curves in class 858k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
858.k1 | 858k1 | [1, 0, 0, -5774401, 5346023177] | [7] | 35280 | \(\Gamma_0(N)\)-optimal |
858.k2 | 858k2 | [1, 0, 0, 16353089, -335543012233] | [] | 246960 |
Rank
sage: E.rank()
The elliptic curves in class 858k have rank \(0\).
Modular form 858.2.a.k
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.