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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 47432.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 47432.x1 | 47432j2 | \([0, -1, 0, -9725536, 11677128828]\) | \(1389715708/11\) | \(805250703437616128\) | \([2]\) | \(2580480\) | \(2.6084\) | |
| 47432.x2 | 47432j1 | \([0, -1, 0, -594876, 190758548]\) | \(-1272112/121\) | \(-2214439434453444352\) | \([2]\) | \(1290240\) | \(2.2618\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 47432.x have rank \(1\).
Complex multiplication
The elliptic curves in class 47432.x do not have complex multiplication.Modular form 47432.2.a.x
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.
