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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 3042.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3042.f1 | 3042d3 | \([1, -1, 0, -31544811, -68185140971]\) | \(986551739719628473/111045168\) | \(390739492089196848\) | \([2]\) | \(215040\) | \(2.7999\) | |
| 3042.f2 | 3042d4 | \([1, -1, 0, -3558411, 877166005]\) | \(1416134368422073/725251155408\) | \(2551972978249941409488\) | \([2]\) | \(215040\) | \(2.7999\) | |
| 3042.f3 | 3042d2 | \([1, -1, 0, -1976571, -1059322523]\) | \(242702053576633/2554695936\) | \(8989320386052055296\) | \([2, 2]\) | \(107520\) | \(2.4533\) | |
| 3042.f4 | 3042d1 | \([1, -1, 0, -29691, -41104283]\) | \(-822656953/207028224\) | \(-728479271550910464\) | \([2]\) | \(53760\) | \(2.1067\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3042.f have rank \(0\).
Complex multiplication
The elliptic curves in class 3042.f do not have complex multiplication.Modular form 3042.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
