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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 45486.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
45486.f1 | 45486n2 | \([1, -1, 0, -246125355, 1488597209477]\) | \(-133179212896925841/240518168576\) | \(-2977859643838427314520064\) | \([]\) | \(10725120\) | \(3.5882\) | |
45486.f2 | 45486n1 | \([1, -1, 0, 181335, -868606291]\) | \(53261199/26353376\) | \(-326281608303959607264\) | \([]\) | \(1532160\) | \(2.6153\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 45486.f have rank \(1\).
Complex multiplication
The elliptic curves in class 45486.f do not have complex multiplication.Modular form 45486.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.