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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 129960.by
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 129960.by1 | 129960bc2 | \([0, 0, 0, -66063, 2455522]\) | \(3631696/1805\) | \(15847702344817920\) | \([2]\) | \(1105920\) | \(1.8014\) | |
| 129960.by2 | 129960bc1 | \([0, 0, 0, 15162, 294937]\) | \(702464/475\) | \(-260652999092400\) | \([2]\) | \(552960\) | \(1.4549\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 129960.by have rank \(1\).
Complex multiplication
The elliptic curves in class 129960.by do not have complex multiplication.Modular form 129960.2.a.by
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.
