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SageMath
sage: E = EllipticCurve("259920.ep1")
sage: E.isogeny_class()
Elliptic curves in class 259920.ep
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 259920.ep1 | 259920ep2 | [0, 0, 0, -525027, -146426654] | [2] | 1474560 | |
| 259920.ep2 | 259920ep1 | [0, 0, 0, -32547, -2327006] | [2] | 737280 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 259920.ep have rank \(0\).
Modular form 259920.2.a.ep
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.
