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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 259182.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 259182.f1 | 259182f1 | \([1, -1, 0, -4044024, -3016538816]\) | \(5663453071972249/231607799808\) | \(299114054822596349952\) | \([2]\) | \(24330240\) | \(2.6946\) | \(\Gamma_0(N)\)-optimal |
| 259182.f2 | 259182f2 | \([1, -1, 0, 1880136, -11114865536]\) | \(569125098462311/41650447874112\) | \(-53790219323919792318528\) | \([2]\) | \(48660480\) | \(3.0412\) |
Rank
sage: E.rank()
The elliptic curves in class 259182.f have rank \(1\).
Complex multiplication
The elliptic curves in class 259182.f do not have complex multiplication.Modular form 259182.2.a.f
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.
