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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 67280.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 67280.f1 | 67280t2 | \([0, -1, 0, -3747776, 2820261760]\) | \(-2841193249/31250\) | \(-64031540859008000000\) | \([]\) | \(2255040\) | \(2.6157\) | |
| 67280.f2 | 67280t1 | \([0, -1, 0, 154464, 20014336]\) | \(198911/200\) | \(-409801861497651200\) | \([]\) | \(751680\) | \(2.0664\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 67280.f have rank \(1\).
Complex multiplication
The elliptic curves in class 67280.f do not have complex multiplication.Modular form 67280.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
