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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 65520d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 65520.bc2 | 65520d1 | \([0, 0, 0, -4656123, 6753539322]\) | \(-553867390580563692/657061767578125\) | \(-13243337493750000000000\) | \([2]\) | \(3999744\) | \(2.9387\) | \(\Gamma_0(N)\)-optimal |
| 65520.bc1 | 65520d2 | \([0, 0, 0, -89031123, 323210414322]\) | \(1936101054887046531846/905403781953125\) | \(36497536287095520000000\) | \([2]\) | \(7999488\) | \(3.2853\) |
Rank
sage: E.rank()
The elliptic curves in class 65520d have rank \(0\).
Complex multiplication
The elliptic curves in class 65520d do not have complex multiplication.Modular form 65520.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
