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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 328560d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 328560.d2 | 328560d1 | \([0, -1, 0, 359184, -869613120]\) | \(913923942103079/58773123072000\) | \(-329565820868886528000\) | \([]\) | \(7776000\) | \(2.6166\) | \(\Gamma_0(N)\)-optimal |
| 328560.d1 | 328560d2 | \([0, -1, 0, -3237216, 23663589120]\) | \(-669076050882037321/42749012087930880\) | \(-239711836358153726853120\) | \([]\) | \(23328000\) | \(3.1659\) |
Rank
sage: E.rank()
The elliptic curves in class 328560d have rank \(0\).
Complex multiplication
The elliptic curves in class 328560d do not have complex multiplication.Modular form 328560.2.a.d
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
